I can't even tell you how much I appreciate these videos. Self-learning math isn't easy by just reading textbooks so it's nice to have your and Professor Leonard's videos to supplement the lectures I'm missing from a standard college curriculum.
THANK YOU Richard for taking the time to "thank the teacher" and "TIP" the teacher too! I hope you continue to find these videos helpful and share this channel whenever you can. Are you just brushing up or taking an online class?
@@profrobbob I hadn't gone beyond intermediate algebra in school, and every time I reach a block in trying to learn anything in any advanced area of a subject, it always seems to come back to my lack of knowing calculus.
That's great news...the world needs more graduates that are passionate about math! Keep opening those doors towards your future and keep your vision clear. Good luck Angela...
I am an international student, and Calculus is my very first Math class in USA. I find it hard to understand in class. Fortunately, I found your channel, haha. You do a very good job. I got to creaet an account to Like and Subscribe :). The way you talk is very clear and easy to understand, I feel that you are very passionate in Math. You got a new Subcriber and Supporter. =)
Who needs to get up in the morning to go to classes when i have all this tutoring in the comfort of my home. I thank you sir, keep doing what you love and keep on inspiring others to see the true beauty of mathematics....
THANK YOU Marlon Maddix for choosing Tarrou's Chalk Talk to watch, learn from and subscribe to! I hope I can continue to inspire others like you...even though you will never hear a teacher support anyone missing class, I do greatly appreciate it when I see students take advantage of the many FREE educational channels on TH-cam that are offered, seek out the help they need, and not just give up!
Thank you so much for taking the time to appreciate all the extra time it takes to key-word and put these lesson in order...and YES, it's all up to us how we choose to post lessons! Thanks for watching and please be sure to share with your friends:)
My teaching style reflects the way I was taught and found it to be the most beneficial learning style for me....so I thank my teacher for that as you thank me! There is so much knowledge out there to choose from, I appreciate that you choose mine...Thank you for supporting and subscribing:)...and good luck towards that degree!
Honestly, how do you only have 95,000 subscribers?? You deserve to have more than a million! Thank you for the lessons Profrobbob, they have helped me so much!
+Kimberly Geronimo we wonder about that ourselves, we've been asking for help to reach 100,000 for 2 years now, about 3,400 to go...lol I think it's because a lot of students don't realize that liking, subbing, sharing and supporting the ads is the best way to support these free educational channels and help us grow! Keep educating your friends about the importance of supporting the free educational channels that help them and we'll keep making videos and aiming for the next milestone...BAM!!!
OMGoodness...that's great news! I certainly can't take all the credit for those grades...you were the one that found my channel and spent all those extra hours learning:) I'd say, together, we make a great team...BAM!!! Keep me posted on that Calc grade:)
You've been helping me succeed in Math for 5 quarters now (currently, I am taking Calculus). Whether I've had questionable professors or excellent ones, you have been a constant source of encouragement and meaningful comprehension. Many sincere thanks to you and your wife for all the hard work. Your channel is wonderful!
You are sincerely welcome Jennifer and many thanks for taking the time to share your appreciation and story with us! Subscribers like you who continue to support our efforts and continually share this channel is a constant reminder why we keep working so hard to grow this free educational channel! If you haven't already, please share this channel and your success story with the head of your math department so all current and future students might benefit as well! THANKS again for all the support..BAM!!!
You are the Messiah of frustrated Calculus students. What you did in 18 minutes, my teacher could not do in a full block of instruction. Thank you so much.
We have a friend in Raleigh but have never visited:( Thanks for the reply...we feel the same...we appreciate when a student acknowledges and replies to our comments as well, like you just did. We have all comments set for approval to keep the channel clean & viewable for all audiences & most of the general comments are answered by me (Mrs Tarrou) & all the math is answered by MR T! Thant's the only way he could teach full time,continue making videos, answer math questions & grow this channel!
I couldn't survive Calculus I without your help. Thanks for generously providing us with the best math tutorials on the planet! I am going to go back and watch from the beginning.
You're welcome and thanks for making me #1 on your subscriber list! This is my first year teaching calc in the classroom and I'm making the videos as fast as I can:) I'm glad to hear that I have a new student from Puerto and please be sure to share my channel with the rest of your class:D
+Roscelle Dalman I have just a little bit for linear algebra here th-cam.com/play/PLGbL7EvScmU4yeJjKaSrp2R7DN6czOV2y.html Unfortunately I don't have any abstract algebra videos.
I apologize for the delay in answering such a nice comment...I saved it to show my wife and it got lost in the sea of emails:( I actually have a few teachers sharing my videos as additional teaching reference for their students. That is quite a compliment to me. I had a teacher in High School that inspired me to want to become a teacher. We are not among the highest paying jobs but the rewards can be very gratifying when you LOVE what you do! Keep me posted with your progress.
Thank you! Your videos are invaluable to me. Calculus is the last class I need to get my associates, but I took College algebra sometime in the early 2000s (2002 I think). Having the ability to watch a video over and over is very helpful. The way you slowly and step by step explain everything is a HUGE help. Keep up the good work.
I love math and I love research....my goal is to combine the two! You can count on me watching as long as possible! A good teacher is very important...and you are one of the best I have seen! Thank you again for taking time to do these videos. :)
You are the only reason I got an A in trig and pre-calc! Thank you so much! You're amazing at explaining things in an enthusiastic, clear way! With your help, I'll be able to get in A in Calculus too!
THAAAANK YOU! I've been watching your videos since Pre Calculus...I didn't have a good professor and they didn't have tutors in summer. Then I found YOU :') I'm taking Calculus now and I still watch your videos! It always helps
You're welcome SharPieFavi ...thanks for choosing #ProfRobBob to watch and learn from! Please remember to like, subscribe and share my channel to help it groW and help others:D
Thank God I found this. Thank you man. Im looking forward to watching all your calc. videos. I've only seen this one but I already feel they are gonna help me so much clear doubts out of the way. Keep them up. Greetings from Puerto
You're the best math professor that ever lived. Thank you for all of your videos. I've learned so much from them. It's such a tremendous help for me since I don't understand everything my professor teaches.
THANK YOU for watching Tonia John and you're welcome! Please share my channel with others in your class who might also be struggling to understand and please remind them to SUBSCRIBE to support these free educational channels and keep them FREE!
Thank-you so much professor! This was a really good introduction video on limits! Really helped me understand how to read the graph and all its components. :-)
I took the test and they told me to the jump in the Calculus class :). Im in Raleigh right now. I was just finding some tutorial about calculus to make sure I understand and I saw your video and absolutely loved it. Hope that your chanel will be popular to the all the students who care about Math :d. and one thing I really like about this chanel is that you take your time to reply comments, I really appreciate that :)
You're welcome:) That's wonderful...you must really love math:) And what is your dream to do with that degree? I won't have videos to help you all the way through but I hope you enjoy learning from Tarrou's Chalk Talk till then!
Thank you. I have been trying to teach myself from a textbook and your videos have helped me understand the concepts so much better than I could have ever done on my own.
mmmcgee1211 you're welcome and thanks for watching, subbing and choosing my channel to help fill in the gaps...congrats on taking on the task of self-teaching...it's nice to be able to help someone so motivated...BAM!!!
You're welcome and THANK YOU...I'm just doing my job! Glad to see you are still watching and thanks for taking the time to send such a glowing compliment:)
That's AWESOME dt, and welcome to my channel! I guess that means you took a lot of math already. May I ask where are you going to school & where are you hear from? I do love teaching and TH-cam has made it possible to expand that passion to the world. I never dreamed when I started this channel 2 years ago that it would grow like it has. My wife started helping a year ago and it is now our dream to groW it to it's potential. I do have approval set on all my comments, that's why the delay.
I haven't been referenced to Batman until now so I'll take that title and add it to my "aka" list! I'm so glad you are getting the help you need from my videos...and if you want to know how you can thank me, just spread the word about my channel to everyone at school! Post it in the student center, on facebook and twitter...just spread the word about me, cause that's how I groW!
You're welcome...and THANK YOU for all the support too! I wish all my students were so self-motivated...BAM!!! When you start school and feel prepared please be sure to share my channel with your class and especially your teacher so ALL future students know where to find this free help:)
I am very pleased with your work and thankful that you have been available to me. I'm in Calc this year so you will help me A LOT! I recommended you today to a girl in my class. She thought your name was cool haha. Thanks again Mr.T
Thank you....the TV spot they did about me was called "Everyday Hero"...glad you think so too! (you can watch it on my home page since you were kind enough to subscribe...and thanks for your support)
You made me LOL...yes, it does look that way:)...I'm glad to see you are still watching my videos and obviously paying close attention too!!!...lol Thanks for your continued support Sunny!
professor RobBob, thank you for a fine/deep analysis on Finding Real Limits Graphical /Numerical Approach in Precalculus/Calculus One. This material will only help students in the beginning of Calculus One. Students will also see the examples in this video all over the Calculus sequence plus all the Engineering and Physics classes.
I'm taking this class online and just by watching the videos given through Mathlab of the explanation made me dread the class and be at loss. Thank you for making this exciting and explaining it the way you do.
You're Welcome yao shen ! Thanks for watching, learning and subbing too...please tell everyone needing math help to do the same and help my channel groW :D
12:26 I think it is quite fascinating that the both-sided-limit seems to exist for that second example piecewise function. My textbook for calculus started with limits definition as follows. "Presuming the function f is defined in the near vicinity of a on boths of its sides, the limit of function f at a, is the limit b" limit as x->a f(x) = b My textbook goes further along this assumption I think, because my textbook says that if the function f (which is a polynomial or a rational function) is defined at a ==> then what follows is that the limit of f, at a, will be the same as the value of the function f(a)... Do you think the piecewise defined function broke my textbook's definition of the limit or what happened there? because my textbook rule would clearly give the wrong answer to your second piecewise-function (x=3 and x is not 3). Using my textbook's rule, limit of f, as x->3 should be = value of function f = f(3). Unless of course your specific piecewise-function clearly goes against the idea of "presuming the function f is defined in the near vicinity of a, which x approaches" My other question would be that... are there any videos about the existence of a limit,, as x->a. For example the following problem was a little bit tough at first for me. find the limit as x->3 for function f , f(x)=(x^2 -9)/[(x-3)^2]
Your textbook sounds like it is making a special case for "function f (which is a polynomial or a rational function)" A piecewise function may have pieces that are polynomials or rational functions, but as a whole it is neither. If you keep watching through my Calculus playlist th-cam.com/play/PL67C119EDA6BDE946.html like say video number 5 you will find an answer to your last question. Check out the Quotient Examples at the end. You may find this page helpful too, www.profrobbob.com/calculus
Hey Mr. T!! My first Cal 1 class is tomorrow and I'm once again taking notes on your vids. Thanks again for the Trig help (got an A) and I putting you out there to my classmates so keep it up Boss! Bam!!!
WOW...that month sure went by fast huh Erik Sanders ?! Sounds like your going into that class prepared and ready for another "A", wish all my students could be like you! Thanks for your continued support and for sharing with your new classmates and we look forward to all those new subscribers...BAM!!!
Daniel McDonald ...welcome back! I hope you have been sharing my channel with others along the way too:) Please remind everyone to like, subscribe, share thru social media and help us keep growing and helping others...BAM!!!
Alpha Tempest another video already?!...you are so welcome...and THANK YOU for watching, learning, liking and subbing to my channel and watching so many lessons already! It's great to see students invest time into studying:)
WOW...thanks for the compliment, it's a big planet out there! And thanks for choosing Tarrou's Chalk Talk to watch and learn from:) Please spread the word about me:D
+Jose Saboya we talked about working on that over summer break but that time flew by so now it's probably on the back burner till next summer:( Thanks for watching though!
Wow I'm learning about this in class and I could not understand my professor.. you explain everything so clearly. your a lifesaver! So watching all your videos throughout my semester! Thank you!!
BAM!!!...that's what I like to hear from my students:) Thanks for subscribing and please feel free to share your experience and my channel with everyone who will listen and help me continue to groW and help other students like yourself from drowning in the sea of math:)
BAM!! Two questions...at 6:00 Is it required that you factor the numerator of the function f(x) = (x^2+x-6)/(x-2) ? Do you have to factor it out? or can you work with it finding the limit without needing to factor? And...will the rules for piecewise funtions like x =/=3 etc.. will those always be x values? Can their be piecewise functions where Y can not equal some number?
Please THANK your friend and thank you for watching and commenting! Please continue to help my channel grow to it's potential by spreading the word to all "your" friends:)
That's awesome...and this is only the beginning of the school year, imagine how much better it's going to get:) Thanks for choosing Tarrou's Chalk Talk to watch and learn from...be sure to share my channel with all your friends too:D
First of all awsome video! I have a question at 13:52 when x is aproaching 3 from the right wouldnt you choose 4, as is a define point in the graph? Thank you very much for your help... I as many others have been watching your videos for a while.
When finding a limit you are finding where the graph is as you APPROACH a value of x in this example, not what the function equals at that value of x. A functions value and the limit may not be equal. At three the functions value is four, but at 3.0000000001 the functions value approaching three from the right is one.
two quick question about those piecewise functions at 12:20. Are either of those example piecewise functions considered to be continuous functions? Are they continuous exactly IN the location of the "funny point" which is isolated from the rest of the graph? I think one high school method of testing the continuity of function was to try to draw the function's graph without lifting the pencil from the paper. If this is not possible, it's not going to be continuous??? (such as with piecewise function???). It appears to me that the piecewise function is not continuuous in that "funny point" which is isolated from the graph
You are generally just looking for points of discontinuity, as these points are the exception to the rest of the Domain where functions are continuous. Each part of that piecewise function are polynomials which are continuous on their entire domain. Your basic idea of continuity is correct. Just don't try that argument in your Calculus class :P
If I was a perfect teacher ALL my students would have "A's"...but THANK YOU for liking, watching, and supporting by subscribing! Please help my channel groW by sharing with others too:D
I had another question on these. At your last example using the T Table, I pluged in those and got different answers, then i went and switched my calculator to Radians and got the answers you were. Sometimes i have trouble with the trig functions so i resort to the t table, do most calculus problems use radians instead of degrees? If i'm doing problems from my teachers would most of them have answers in radians?
Mr Tarrou, at 11:38 how is -4 the limit if it is included? In your previous examples you had open dots meaning it is less than or greater than a number but that number cannot be included thus making that number the limit. But if you have less/greater than or equal to, then that number could be included, and if it is included then wouldn't that not make it a limit because it can still be included? Also wouldn't that apply to any function that includes the closed dot? Unless there's more to what makes something considered a "limit"
I spend a lot of time trying to explain that there is a difference between a functions value at c, and f(c), because they CAN be different. However more often than not, within a function's domain f(c) will equal the limit as x approaches c of f(x)... anywhere the function is continuous:)
Hey professor, just confused as to where the numbers come from when you make the T table at the end of the video. Mainly the bottom row. Thanks for all that you do.
Send me a message through my Facebook fan page. I am really overwhelmed right now at work, but if I can easily answer your question I will tomorrow...if it is too tough it may be a few days.
Your welcome...and remember, I can be your math teacher anytime you want to click a button and learn!! Thank you for watching and please be sure to share with your friends if you find my videos helpful...I grow through your support:D Thank youuuuuuuuuuuuuuuu too.
Hi prof.. Great video. One problem: why is it that in your last example- when i replace x with -0.01 or any of the other values, I do not get those y values?
ProfRobBob thank you for the video but I have a question my eco teacher asked me ,even though that was irrelevant to what we study in this class, anyway, my question is why we can't cube the value 1.1 he even said try it on your calculator and it'll pass away. thank u again I always watch your vids
This is your PSA to turn on captions when watching these videos! You can make them small and unobtrusive, but sometimes there are helpful notes in them!
On a basic F(x)=x^2, why is the limit as h approaches 0 always zero. In other words, why do you sub 0 for h so f prime of x is alwats just 2x, not 2x+h? Thanks
This was one of my earlier videos Alpha Jalloh before I felt comfortable in front of the camera...don't worry, there are plenty of jumps in my videos to follow...BAM!!! Thanks for subbing...please spread the word:D
+TheJet 1 A function can be undefined at a point where the two sided limit exists like at a hole in the graph. So while I don't know what book or teacher you are learning from, I would say that yes there is a difference.
The hole goes were the equation would be undefined (i.e. the denominator is equal to zero when you plug in X). So if your denominator was x+3 the hole would be when x = -3.
Every time I see dislikes on these videos, I don't get it. What are they, jealous professors or something? How does one dislike these videos?! these vids are why half of the student population understand calculus!
What a nice thing to say…and THANK YOU for taking the time to say it! Everyone has the right to their opinion. I will continue to do the best job at teaching and posting videos that I know how to and appreciate the support of viewers like yourself. Please continue your support by SUBSCRIBING and sharing my channel with your friends and classmates:D Thanks!
ProfRobBob You got it, I'm subscribed and content. I try to watch each video from the chapter I'm working on before my class touches the subject. It reduces my stress level Lol It's funny because it's not about the grade anymore. I actually WANT to understand this universal and powerful language: math. Life just makes more sense.
Dragus Calliforous BAM!!!...words every teacher would love to hear form their students "working ahead" is not in most students vocabulary sad to say! I wish all my students were even half as motivated as you my friend! Thanks again for the support...our dream is to someday see a "M" next to my subscriber count:) If you're gonna dream, dream BIG!!!
Actually the example is set up correctly. Put your graphing calculator in radian mode and graph you see a graph that has a hole at (0,1). Actually you will probably not see the hole in the graph, but there is one because you cannot divide by zero.
I have some trouble with example 5, plugging the same x values you chose in the equation f(x) = sin(x)/x i get completely different y values. sin(-0.03)/(-0.03) = 0.01745329172 nothing close 0.099985! Am i doing it wrong or has my calculator lost it ?! Help ! Thank you.
I can't even tell you how much I appreciate these videos. Self-learning math isn't easy by just reading textbooks so it's nice to have your and Professor Leonard's videos to supplement the lectures I'm missing from a standard college curriculum.
THANK YOU Richard for taking the time to "thank the teacher" and "TIP" the teacher too!
I hope you continue to find these videos helpful and share this channel whenever you can.
Are you just brushing up or taking an online class?
@@profrobbob I hadn't gone beyond intermediate algebra in school, and every time I reach a block in trying to learn anything in any advanced area of a subject, it always seems to come back to my lack of knowing calculus.
@@profrobbob yesh
That's great news...the world needs more graduates that are passionate about math! Keep opening those doors towards your future and keep your vision clear. Good luck Angela...
I am an international student, and Calculus is my very first Math class in USA. I find it hard to understand in class. Fortunately, I found your channel, haha. You do a very good job. I got to creaet an account to Like and Subscribe :). The way you talk is very clear and easy to understand, I feel that you are very passionate in Math. You got a new Subcriber and Supporter. =)
Who needs to get up in the morning to go to classes when i have all this tutoring in the comfort of my home. I thank you sir, keep doing what you love and keep on inspiring others to see the true beauty of mathematics....
THANK YOU Marlon Maddix for choosing Tarrou's Chalk Talk to watch, learn from and subscribe to! I hope I can continue to inspire others like you...even though you will never hear a teacher support anyone missing class, I do greatly appreciate it when I see students take advantage of the many FREE educational channels on TH-cam that are offered, seek out the help they need, and not just give up!
Thank you so much for taking the time to appreciate all the extra time it takes to key-word and put these lesson in order...and YES, it's all up to us how we choose to post lessons! Thanks for watching and please be sure to share with your friends:)
My teaching style reflects the way I was taught and found it to be the most beneficial learning style for me....so I thank my teacher for that as you thank me! There is so much knowledge out there to choose from, I appreciate that you choose mine...Thank you for supporting and subscribing:)...and good luck towards that degree!
Honestly, how do you only have 95,000 subscribers?? You deserve to have more than a million! Thank you for the lessons Profrobbob, they have helped me so much!
+Kimberly Geronimo we wonder about that ourselves, we've been asking for help to reach 100,000 for 2 years now, about 3,400 to go...lol
I think it's because a lot of students don't realize that liking, subbing, sharing and supporting the ads is the best way to support these free educational channels and help us grow! Keep educating your friends about the importance of supporting the free educational channels that help them and we'll keep making videos and aiming for the next milestone...BAM!!!
OMGoodness...that's great news! I certainly can't take all the credit for those grades...you were the one that found my channel and spent all those extra hours learning:) I'd say, together, we make a great team...BAM!!!
Keep me posted on that Calc grade:)
You've been helping me succeed in Math for 5 quarters now (currently, I am taking Calculus). Whether I've had questionable professors or excellent ones, you have been a constant source of encouragement and meaningful comprehension. Many sincere thanks to you and your wife for all the hard work. Your channel is wonderful!
You are sincerely welcome Jennifer and many thanks for taking the time to share your appreciation and story with us! Subscribers like you who continue to support our efforts and continually share this channel is a constant reminder why we keep working so hard to grow this free educational channel!
If you haven't already, please share this channel and your success story with the head of your math department so all current and future students might benefit as well!
THANKS again for all the support..BAM!!!
You are the Messiah of frustrated Calculus students. What you did in 18 minutes, my teacher could not do in a full block of instruction. Thank you so much.
We have a friend in Raleigh but have never visited:( Thanks for the reply...we feel the same...we appreciate when a student acknowledges and replies to our comments as well, like you just did. We have all comments set for approval to keep the channel clean & viewable for all audiences & most of the general comments are answered by me (Mrs Tarrou) & all the math is answered by MR T! Thant's the only way he could teach full time,continue making videos, answer math questions & grow this channel!
I couldn't survive Calculus I without your help. Thanks for generously providing us with the best math tutorials on the planet! I am going to go back and watch from the beginning.
You're welcome and thanks for making me #1 on your subscriber list! This is my first year teaching calc in the classroom and I'm making the videos as fast as I can:) I'm glad to hear that I have a new student from Puerto and please be sure to share my channel with the rest of your class:D
i learn better with your videos.. Thank you very much for taking the time.. Do you have videos for linear and abstract algebra?
+Roscelle Dalman I have just a little bit for linear algebra here th-cam.com/play/PLGbL7EvScmU4yeJjKaSrp2R7DN6czOV2y.html Unfortunately I don't have any abstract algebra videos.
I apologize for the delay in answering such a nice comment...I saved it to show my wife and it got lost in the sea of emails:( I actually have a few teachers sharing my videos as additional teaching reference for their students. That is quite a compliment to me. I had a teacher in High School that inspired me to want to become a teacher. We are not among the highest paying jobs but the rewards can be very gratifying when you LOVE what you do! Keep me posted with your progress.
Thank you:) I hope you do great in your class!
Thank you! Your videos are invaluable to me. Calculus is the last class I need to get my associates, but I took College algebra sometime in the early 2000s (2002 I think). Having the ability to watch a video over and over is very helpful. The way you slowly and step by step explain everything is a HUGE help. Keep up the good work.
I love math and I love research....my goal is to combine the two! You can count on me watching as long as possible! A good teacher is very important...and you are one of the best I have seen! Thank you again for taking time to do these videos. :)
You are the only reason I got an A in trig and pre-calc! Thank you so much! You're amazing at explaining things in an enthusiastic, clear way! With your help, I'll be able to get in A in Calculus too!
I am truly happy you are on youtube because you are the reason I got through trig last year and will be the reason I get through Calculus this year!
THAAAANK YOU! I've been watching your videos since Pre Calculus...I didn't have a good professor and they didn't have tutors in summer. Then I found YOU :') I'm taking Calculus now and I still watch your videos! It always helps
You're welcome SharPieFavi ...thanks for choosing #ProfRobBob to watch and learn from!
Please remember to like, subscribe and share my channel to help it groW and help others:D
Thank God I found this. Thank you man. Im looking forward to watching all your calc. videos. I've only seen this one but I already feel they are gonna help me so much clear doubts out of the way. Keep them up. Greetings from Puerto
ProfRobBob you are a hero. i don't know how i can thank you. you are like the Batman of engineering students
My friend recommended that I watch your videos, and I have to say.. you seriously rock.
You're the best math professor that ever lived. Thank you for all of your videos. I've learned so much from them. It's such a tremendous help for me since I don't understand everything my professor teaches.
THANK YOU for watching Tonia John and you're welcome!
Please share my channel with others in your class who might also be struggling to understand and please remind them to SUBSCRIBE to support these free educational channels and keep them FREE!
Thank you very much. I really appreciate you watching and the nice comment. I will do my best to help:)
thank you so much sir. the way you teach is easy to understand because you makes the concepts very clear.
Thank-you so much professor! This was a really good introduction video on limits! Really helped me understand how to read the graph and all its components. :-)
You're welcome...glad I could help!
Thanks for tuning in...please like, sub ad share this free resource with everyone!!!
Thank you! I passed my trig course last semester because of you and I am back for your calc videos :)
I took the test and they told me to the jump in the Calculus class :). Im in Raleigh right now. I was just finding some tutorial about calculus to make sure I understand and I saw your video and absolutely loved it. Hope that your chanel will be popular to the all the students who care about Math :d. and one thing I really like about this chanel is that you take your time to reply comments, I really appreciate that :)
You're welcome:) That's wonderful...you must really love math:) And what is your dream to do with that degree? I won't have videos to help you all the way through but I hope you enjoy learning from Tarrou's Chalk Talk till then!
Thank you. I have been trying to teach myself from a textbook and your videos have helped me understand the concepts so much better than I could have ever done on my own.
mmmcgee1211 you're welcome and thanks for watching, subbing and choosing my channel to help fill in the gaps...congrats on taking on the task of self-teaching...it's nice to be able to help someone so motivated...BAM!!!
I e-mailed the link to my former college algebra professor. She said that you do a good job and that she'd share your link with future students. :)
mmmcgee1211 THANKS...that's awesome and a great way to help us groW!!!
We really appreciate the share:)
Another great video. I have never thumbed up so much on any one channel before. Well done sir!!
Haven't had many students comment as much either...glad you are enjoying learning so much from these lessons!
You're welcome and THANK YOU...I'm just doing my job! Glad to see you are still watching and thanks for taking the time to send such a glowing compliment:)
That's AWESOME dt, and welcome to my channel! I guess that means you took a lot of math already. May I ask where are you going to school & where are you hear from? I do love teaching and TH-cam has made it possible to expand that passion to the world. I never dreamed when I started this channel 2 years ago that it would grow like it has. My wife started helping a year ago and it is now our dream to groW it to it's potential. I do have approval set on all my comments, that's why the delay.
I haven't been referenced to Batman until now so I'll take that title and add it to my "aka" list!
I'm so glad you are getting the help you need from my videos...and if you want to know how you can thank me, just spread the word about my channel to everyone at school! Post it in the student center, on facebook and twitter...just spread the word about me, cause that's how I groW!
Thank you! The enthusiasm is appreciated!
+Aschalew Teka so is the sub and studying with Tarrou's Chalk Talk...BAM!!!
Thank you very much professor RobBob. You are an amazing person. I like to learn from you because you explain very clear.
Lynn Kang you're welcome, thanks for watching!
Watching your videos every day this summer before calc class in august. Trying to learn the material b4 class begins. Thankyou!!
You're welcome...and THANK YOU for all the support too!
I wish all my students were so self-motivated...BAM!!!
When you start school and feel prepared please be sure to share my channel with your class and especially your teacher so ALL future students know where to find this free help:)
Your welcome. I hope you do great on your test...when you get to take it.
I am very pleased with your work and thankful that you have been available to me. I'm in Calc this year so you will help me A LOT! I recommended you today to a girl in my class. She thought your name was cool haha. Thanks again Mr.T
Your explanation to the topic is excellent.
Thanks for watching...please sub and share this channel with everyone:D
Thank you....the TV spot they did about me was called "Everyday Hero"...glad you think so too! (you can watch it on my home page since you were kind enough to subscribe...and thanks for your support)
You made me LOL...yes, it does look that way:)...I'm glad to see you are still watching my videos and obviously paying close attention too!!!...lol Thanks for your continued support Sunny!
professor RobBob, thank you for a fine/deep analysis on Finding Real Limits Graphical /Numerical Approach in Precalculus/Calculus One. This material will only help students in the beginning of Calculus One. Students will also see the examples in this video all over the Calculus sequence plus all the Engineering and Physics classes.
I'm taking this class online and just by watching the videos given through Mathlab of the explanation made me dread the class and be at loss. Thank you for making this exciting and explaining it the way you do.
You're very welcome and thanks for seeking outside help and choosing this channel...good luck and go pass that class like BAM!!!
THANK YOU SIR, I've watched your video since the trig class!
You're Welcome yao shen !
Thanks for watching, learning and subbing too...please tell everyone needing math help to do the same and help my channel groW :D
12:26 I think it is quite fascinating that the both-sided-limit seems to exist for that second example piecewise function. My textbook for calculus started with limits definition as follows.
"Presuming the function f is defined in the near vicinity of a on boths of its sides, the limit of function f at a, is the limit b" limit as x->a f(x) = b
My textbook goes further along this assumption I think, because my textbook says that if the function f (which is a polynomial or a rational function) is defined at a ==> then what follows is that the limit of f, at a, will be the same as the value of the function f(a)... Do you think the piecewise defined function broke my textbook's definition of the limit or what happened there?
because my textbook rule would clearly give the wrong answer to your second piecewise-function (x=3 and x is not 3). Using my textbook's rule, limit of f, as x->3 should be = value of function f = f(3). Unless of course your specific piecewise-function clearly goes against the idea of "presuming the function f is defined in the near vicinity of a, which x approaches"
My other question would be that... are there any videos about the existence of a limit,, as x->a. For example the following problem was a little bit tough at first for me.
find the limit as x->3 for function f , f(x)=(x^2 -9)/[(x-3)^2]
Your textbook sounds like it is making a special case for "function f (which is a polynomial or a rational function)" A piecewise function may have pieces that are polynomials or rational functions, but as a whole it is neither. If you keep watching through my Calculus playlist th-cam.com/play/PL67C119EDA6BDE946.html like say video number 5 you will find an answer to your last question. Check out the Quotient Examples at the end. You may find this page helpful too, www.profrobbob.com/calculus
great for my test tomorrow! thanks mr tarrou
Hey Mr. T!! My first Cal 1 class is tomorrow and I'm once again taking notes on your vids. Thanks again for the Trig help (got an A) and I putting you out there to my classmates so keep it up Boss! Bam!!!
WOW...that month sure went by fast huh Erik Sanders ?! Sounds like your going into that class prepared and ready for another "A", wish all my students could be like you!
Thanks for your continued support and for sharing with your new classmates and we look forward to all those new subscribers...BAM!!!
Daniel McDonald ...welcome back!
I hope you have been sharing my channel with others along the way too:)
Please remind everyone to like, subscribe, share thru social media and help us keep growing and helping others...BAM!!!
You've helped me so much! Thank you. Limits can be so tricky....
Alpha Tempest another video already?!...you are so welcome...and THANK YOU for watching, learning, liking and subbing to my channel and watching so many lessons already! It's great to see students invest time into studying:)
WOW...thanks for the compliment, it's a big planet out there! And thanks for choosing Tarrou's Chalk Talk to watch and learn from:) Please spread the word about me:D
How great you are to present calculus, your writing is nice and I even easier to understand your presentation. Thank you for Prof RobBob, GBU
THANKS for studying and subbing to my channel!
Please tell all your friends and classmates to watch and do the same:D
College entrance exams is near and we don't have calculus class so this is really helpful! Thank you and God bless :)
Thanks for studying and subbing Riz...please spread the word thru all your social media so all your friends can watch and do the same...BAM!!!
Great Videos!!! i only wish if we could get some worksheets
+Jose Saboya we talked about working on that over summer break but that time flew by so now it's probably on the back burner till next summer:(
Thanks for watching though!
Great video!
THANKS for liking and learning Dan Hoang !
Thank you Mr. T..................JJ
=)
Wow I'm learning about this in class and I could not understand my professor.. you explain everything so clearly. your a lifesaver! So watching all your videos throughout my semester! Thank you!!
BAM!!!...that's what I like to hear from my students:)
Thanks for subscribing and please feel free to share your experience and my channel with everyone who will listen and help me continue to groW and help other students like yourself from drowning in the sea of math:)
ProfRobBob
Oh! so that's what you're always saying (Bam!!!)...hilariously funny.
BAM!! Two questions...at 6:00 Is it required that you factor the numerator of the function f(x) = (x^2+x-6)/(x-2) ? Do you have to factor it out? or can you work with it finding the limit without needing to factor? And...will the rules for piecewise funtions like x =/=3 etc.. will those always be x values? Can their be piecewise functions where Y can not equal some number?
thank you too for subscribing!
Please THANK your friend and thank you for watching and commenting! Please continue to help my channel grow to it's potential by spreading the word to all "your" friends:)
That's awesome...and this is only the beginning of the school year, imagine how much better it's going to get:)
Thanks for choosing Tarrou's Chalk Talk to watch and learn from...be sure to share my channel with all your friends too:D
Thanks for doing that graph on SinX/X example-Things just dropped into place when you did that-JJ
john james you're welcome. And thank you for watching, learning and subbing!
Please spread the word:D
Very helful! I often get confused by the notation, :( but watching your videos help a lot :)
luna SV thanks for watching, learning, liking and subbing!
First of all awsome video! I have a question at 13:52 when x is aproaching 3 from the right wouldnt you choose 4, as is a define point in the graph? Thank you very much for your help... I as many others have been watching your videos for a while.
When finding a limit you are finding where the graph is as you APPROACH a value of x in this example, not what the function equals at that value of x. A functions value and the limit may not be equal. At three the functions value is four, but at 3.0000000001 the functions value approaching three from the right is one.
Thanks...tends to keep the mistakes to a minimum when students can read it:)
two quick question about those piecewise functions at 12:20. Are either of those example piecewise functions considered to be continuous functions? Are they continuous exactly IN the location of the "funny point" which is isolated from the rest of the graph?
I think one high school method of testing the continuity of function was to try to draw the function's graph without lifting the pencil from the paper. If this is not possible, it's not going to be continuous??? (such as with piecewise function???). It appears to me that the piecewise function is not continuuous in that "funny point" which is isolated from the graph
You are generally just looking for points of discontinuity, as these points are the exception to the rest of the Domain where functions are continuous. Each part of that piecewise function are polynomials which are continuous on their entire domain. Your basic idea of continuity is correct. Just don't try that argument in your Calculus class :P
CONGRATULATIONS...And THANK YOU for returning to Tarrou's Chalk Talk to learn more math:)
Don't forget to share with others too:D
You are my hero. Seriously. :)
You are a perfect teacher (Y) :)
If I was a perfect teacher ALL my students would have "A's"...but THANK YOU for liking, watching, and supporting by subscribing! Please help my channel groW by sharing with others too:D
great video!!!!!
You're welcome!
I had another question on these. At your last example using the T Table, I pluged in those and got different answers, then i went and switched my calculator to Radians and got the answers you were. Sometimes i have trouble with the trig functions so i resort to the t table, do most calculus problems use radians instead of degrees? If i'm doing problems from my teachers would most of them have answers in radians?
Mr Tarrou, at 11:38 how is -4 the limit if it is included? In your previous examples you had open dots meaning it is less than or greater than a number but that number cannot be included thus making that number the limit. But if you have less/greater than or equal to, then that number could be included, and if it is included then wouldn't that not make it a limit because it can still be included? Also wouldn't that apply to any function that includes the closed dot? Unless there's more to what makes something considered a "limit"
I spend a lot of time trying to explain that there is a difference between a functions value at c, and f(c), because they CAN be different. However more often than not, within a function's domain f(c) will equal the limit as x approaches c of f(x)... anywhere the function is continuous:)
Hey professor, just confused as to where the numbers come from when you make the T table at the end of the video. Mainly the bottom row. Thanks for all that you do.
thanks prof
Thanks for subbing too!
Send me a message through my Facebook fan page. I am really overwhelmed right now at work, but if I can easily answer your question I will tomorrow...if it is too tough it may be a few days.
Your welcome...and remember, I can be your math teacher anytime you want to click a button and learn!! Thank you for watching and please be sure to share with your friends if you find my videos helpful...I grow through your support:D Thank youuuuuuuuuuuuuuuu too.
I have a test on Sunday and I'm hoping that this video will help me understand every little thing.
Hope you pass that test like BAM!!!
Thanks to you, I'm on my way to a Master's in Mathematics!
Did you get your degree yet?
Hi prof.. Great video.
One problem: why is it that in your last example- when i replace x with -0.01 or any of the other values, I do not get those y values?
can i show you a limit question am stuck on??????
ProfRobBob thank you for the video but I have a question my eco teacher asked me ,even though that was irrelevant to what we study in this class, anyway, my question is why we can't cube the value 1.1 he even said try it on your calculator and it'll pass away. thank u again I always watch your vids
This is your PSA to turn on captions when watching these videos! You can make them small and unobtrusive, but sometimes there are helpful notes in them!
Can we get a video explaining Riemann's sum and finding the area between two functions?
www.profrobbob.com/calculus/area-between-curves
www.profrobbob.com/calculus/integration-an-introduction
Today's #Calculus lesson
ProfRobBob A new semester of college and im taking Calculus this year. You always teach better than my professors so I cant wait to learn from you!
HG Gha Thanks for the continued viewership!
Now go pass that Calc class like BAM!!!
On a basic F(x)=x^2, why is the limit as h approaches 0 always zero. In other words, why do you sub 0 for h so f prime of x is alwats just 2x, not 2x+h? Thanks
12:06 Haha :) "And I've taken the privilege or the ... uhh ... privilege? Uhh whatever."
Nice catch...wish all my students paid attention like that:)
@@profrobbob The occasional humor keeps the student more engaged :)
I hope so:)@@rwharrington87
Bam!!!!!!!!!!! Oh yeah!!!!! This is the stuff!!!!!!!!
Your teachers are lucky to have such an awesome student:)
Merci encore!! Why y didn't jump in this video!??
This was one of my earlier videos Alpha Jalloh before I felt comfortable in front of the camera...don't worry, there are plenty of jumps in my videos to follow...BAM!!!
Thanks for subbing...please spread the word:D
Is there any difference between the terms Does Not Exist (DNE) and the term undefined?
+TheJet 1 A function can be undefined at a point where the two sided limit exists like at a hole in the graph. So while I don't know what book or teacher you are learning from, I would say that yes there is a difference.
what I'm really confused about is, how or where do you know where to put the hole on the graph?
The hole goes were the equation would be undefined (i.e. the denominator is equal to zero when you plug in X). So if your denominator was x+3 the hole would be when x = -3.
Jose Cossio Thanks for the help:)
Hey man i love you.
Please like, sub and share the love and this free channel with everyone...BAM!!!
I'm so used to watching your videos at 2x speed normal speed feels like slow motion.
Thanks for watching at "any" speed..BAM!!!
Every time I see dislikes on these videos, I don't get it. What are they, jealous professors or something? How does one dislike these videos?! these vids are why half of the student population understand calculus!
What a nice thing to say…and THANK YOU for taking the time to say it!
Everyone has the right to their opinion. I will continue to do the best job at teaching and posting videos that I know how to and appreciate the support of viewers like yourself. Please continue your support by SUBSCRIBING and sharing my channel with your friends and classmates:D Thanks!
ProfRobBob
You got it, I'm subscribed and content. I try to watch each video from the chapter I'm working on before my class touches the subject. It reduces my stress level Lol
It's funny because it's not about the grade anymore. I actually WANT to understand this universal and powerful language: math. Life just makes more sense.
Dragus Calliforous BAM!!!...words every teacher would love to hear form their students "working ahead" is not in most students vocabulary sad to say! I wish all my students were even half as motivated as you my friend!
Thanks again for the support...our dream is to someday see a "M" next to my subscriber count:) If you're gonna dream, dream BIG!!!
You got it! I am spreading the word.
I can't thank you enough, thanks again. :)
Dragus Calliforous You're always welcome:)
BAM!!!...we can see that "M" in our future now!
Love You :))
+AA M thanks for watching...I hope you'll love this channel enough to like, sub, support the ads and share it with everyone...BAM!!!
i believe you mean cosine not sine.....for your fifth example...
Omg he did I was like wtffff
Actually the example is set up correctly. Put your graphing calculator in radian mode and graph you see a graph that has a hole at (0,1). Actually you will probably not see the hole in the graph, but there is one because you cannot divide by zero.
I have some trouble with example 5, plugging the same x values you chose in the equation f(x) = sin(x)/x i get completely different y values. sin(-0.03)/(-0.03) = 0.01745329172 nothing close 0.099985! Am i doing it wrong or has my calculator lost it ?! Help ! Thank you.
Your calculator is in degree mode, it should be in radians:) I do that all the time. Calculus is done in radians because it has no unit of measure.
ProfRobBob Thankyou so much =) !
xxTHE_GAMER_HDXX you're welcome:)
Please keep sharing my channel with others and remind them to SUBSCRIBE:D
4:44 hehe you are popping a parabola pimple xD