Best Explanation ever!!! I'm taking Calculus 1 in university and unfortunately professors don't get a lot of time to elaborate all their steps. But this video does elaborate and puts it in very good simple terms allowing anyone to understand this topic and making Calculus a more fun course. Very pleased, please keep posting your content in the same format, as I find the best teachers tend to go back and explain old rules and refresh the students of the reasoning behind every step, as not everyone can remember them, and in Calculus you certainly need to remember everything you have learned in the past otherwise your screwed.
Your explanation for why you placed a negative in front of the square root of (1/x^6) was so clear. I stumbled on this video while I was studying for my first calc exam. And B/c i watched this video , I was the only one in all 3 of my prof's classes to answer one of questions correctly. Thank you so much
Math tutors at my school couldn't help me with a few Calculus problems I had and within 10 minutes of finding your channel I was able to solve them all. Thank you.
@I3lak i dont know what you mean. again, squaring some arbitrary function to produce a new one does exactly that: produces a new one. it is not the same thing any more.
Thank you so so so soooo much!! 🙏 Ive been trying for 2 hours how to understand what I was doing wrong on my assignment on Khan Academy. The video that my teacher assigned for that assignment literally did not go over the different ways to solve the problems. But thanks to your “negative infinity & odd power = positive” & “negative infinity & even power = negative”, I finally understand how to do this! You did what Khan Academy could not, and for that I thank you from the bottom of my heart. Calculus is painful...
I was staring at that x^2 in the radical forever wondering how they got it in there if they divide by x. The book doesn't really explain it well. You explain in just minutes and bam! Thank you so much!
my calc teacher is soooo baddd at teaching omg + boring (she is obssessed with cows too)..weird a sshit...dude all i gotta say is that you have taught me what she tried teaching me over like 3 months..thank you so much and keep up the good work man...so glad there are people like you who are willing to give time for others you freaking rock!
patrickJMT The math never changes, but the moment of elation that you get when everything makes sense is the greatest feeling of all! I was struggling with the negative sign on the odd powers for a good two hours, then I watched this video and it all made sense!
your prof is certainly correct. however, since we are doing x -->+infinity, the x value is already assumed to be positive, so we do not need to worry about +/- x... only +x
Thank you! I was really confused about radicals in the denominator when the limit approaches negative infinity. My shitty calculus book has problems like this but doesn't explain how to approach them.
thanks alot, i have been sitting for hours and days trying to figure out things for my self with my 1000 page math book and long boring lectures without any result, but your videos really helped me to finaly understand it =D
@ Lou, in this problem, square root of x^2 is indeed equal to x because we're being asked for the limit of the function WHEN x approaches positive infinity.
I watched the first example to find out how to do my assignment. I did all of the questions on it and then watched the rest of the video. turns out the second example was a question on my assignment and I had lost the negative sign in my work. thanks for the help!
I like that his radicals have a radical (end) edge better. and yes, HOW do you notice these things, instead of the problems he's working for us, lmao....
my pleasure! and... you live in austin too?! gooooooooooooooooo austin!! moved here two years ago and totally love it, although the heat is starting to make me go insane i think...
Just thought you should know this video is WAY more helpful than the teaching process at school and Khan Academy’s demonstration of this topic. Thank you!!
It would be awesome if you showed a problem that had a radical over the entire equation! I figured it out tho watching this video... thanks for all your vids Patrick, really helps me out!
Thanks for explaining the sqrt(a) * sqrt(b) = sqrt(ab). I knew that rule, but didn't know I needed to use it to divide the radical by x. Turning x into sqrt(1/x^2). Was always wondering where the x^2 was coming from.
As other people have stated, since the sqrt of x^6 is abs x^3, you can determine that x^3 is negative when x approaches negative infinity in this video. That's how the negative 1 comes in
thank you so much for your explanation of the negative sign at x approaching negative infinity! my teacher did not explain it well and i got really confused at first, but now after watching this it becomes so logical :)
Hi Patrick, what happens if numbers are raised to x power or x-root when x approaches infinity? Example: 1) Limit 1^x as x->inf. How should we go about doing it? 2) Limit x->inf (2^x + 3^x + 5^x + 7^x + 11^x + 13^x)^(1/x)
You are awesome! I had a similar question in my midterm as your second example, but I had no idea why there was a negative in the answer. You have cleared it up, just in time for my final exam upcoming in a week. Thanks for your videos!
Thank you for posting these videos. They are so helpful for studying. I was wondering what you would do if the radical was on the numerator rather than the denominator?
Man, i wish I could stuff you in my backpack and carry you around :( You explain math so well...right now I'm in a class with a prof that's almost impossible to understand. I don't know how else I'd be learning calc on my own without youtube
how do you begin to think like that, the algebraic manipulation you did: 1/x^2 = squ(1/x^4) to get the two expressions under the same radical. I had a similar problem and I would have never fancied to do that.
that is incorrect algebra; you can not square the numerator and denominator and have it be equivalent (in general). 2/3 is not the same as 2^2/3^2 ; you are multiplying the numerator by 2 but the denominator by 3. this is a pretty common mistake though
Wow, even though I'm kinda really late but this video saved me and I am really grateful. I'm really happy that I found the right video for my math problem, thanks!
How about radicals without a denominator such as sqrt(4x^2-2x+1)-2x as lim x->inf; multiplying by conjugate of 1 doesn't work, nor do normal methods. It evaluates to -1/2, but how can you solve it?
i just asked the same question. There must be a reason, because when you graph this function, you see that it does tend to -1 as x goes to neg infinity. Id just like a less "hand wavey" explanation :) Even my professor could not really explain why. Perhaps because it is an odd function?. The numerator is x^3, which does produce the behavior that would require a negative limit.
well, you have to remember that you are taking a limit: the basic idea here is that if you put larger and larger values for x into the function (that is , as x --> infinity), the values of 4/x^2 and 3/x will get arbitrarily close to zero.
@patrickJMT lmao!!!! omg i just wanted to tell you thank you for taking time out to do these videos. I swear i was failing this class an i'm determined to get an A. Thank yous soo much. Idk if u know how much it means to me, cause i suck @ math :(
What about if the degree under the radical was odd? You only gave examples of it when it was even. Do you still do the same thing except divide by the degree over two (because of the square root) times the radical x? ex. denominator = sqrt(x^3 + 7) would you divide by x*sqrt(x)?
I cant believe this video was made 12 yrs ago. I was like jinjja? 😲 Anyways 'til now this helps me a lot. Especially this time of crisis where we're having online class. We have to teach ourselves. 😔😔 Thank you really! This might save me from my exam next week ♡♡♡
I have been watching your videos for 4 years now :) Thank you! much more helpful than kahn academy :) My question. in your second example, you show that (1/x^2)^1/2 = 1/x, and because the limit goes to neg infinity, we tack on a -, such that -(1/x^2)^1/2 = -(1/x). Wouldn't the same then be true for the numerator? -(1/x^2)*x^2 would yield -1 in the numerator, and then -1 in the denominator, resulting in the limit being 1, and not -1? Why do we only tack the neg sign in the denominator?
in the second question ,you divided the numerator with x^3. were you not supposed to divide it with -x^3 just like you divided in the denominator with -x^3 since the limit is going to negative infinity and also that the power isn't even?
Fantastic video! Except, I'm a little confused at 5:37 when you found that the square root of 1/x^6 is the same as 1/x^3. Why is that? I would have thought it would be 1/x^9 because the square root of 9 is 3. Could you explain this please?
sorry about the double comments, my internet was acting up. I also wanted to know what do you do if the radical is like the sqrt( 9x^2 + 4). Do you keep the 9 and take the root of it?
Why do u first need to turn the thing you are dividing by in the denominator into a radical before you think about what would happen the limit as approaches negative or positive infinity
is it wrong if i square both numerator and denominator to get red of the radical sign? this did work with the first example but it did not with second one. i don't know why?
for the second example, couldn't you technically say that the degree of the numerator (which is x^3) and denominator (which is x^(6/2)=x^3) are equal, thus the limit would equal the ratio of the coefficients of those terms which would be 1/1 = 1? but the solution should apparently be -1. i'm just a little confused on why that rational function trick doesn't work for example 2. thanks so much for all your help! your videos are awesome
Well since you're approaching negative infinity, that is how the trick would result in -1 I believe. ...I am answering 8 months later, so I'm wondering if this advice is still applicable haha
Best Explanation ever!!! I'm taking Calculus 1 in university and unfortunately professors don't get a lot of time to elaborate all their steps. But this video does elaborate and puts it in very good simple terms allowing anyone to understand this topic and making Calculus a more fun course. Very pleased, please keep posting your content in the same format, as I find the best teachers tend to go back and explain old rules and refresh the students of the reasoning behind every step, as not everyone can remember them, and in Calculus you certainly need to remember everything you have learned in the past otherwise your screwed.
11 years passed and still super helpful, thank you!
The explanation on why 1/x^2 will go positive and 1/x^3 will go negative was a huge help. Much appreciated!!!!
Your explanation for why you placed a negative in front of the square root of (1/x^6) was so clear. I stumbled on this video while I was studying for my first calc exam. And B/c i watched this video , I was the only one in all 3 of my prof's classes to answer one of questions correctly. Thank you so much
Math tutors at my school couldn't help me with a few Calculus problems I had and within 10 minutes of finding your channel I was able to solve them all. Thank you.
@I3lak i dont know what you mean. again, squaring some arbitrary function to produce a new one does exactly that: produces a new one. it is not the same thing any more.
Oh wow ma' man.
This video explanation helped me out so much.
This problem is no problem any more.
Thanks Patrick!
Dude, your explanation on the negative infinity really helped me out! THANK YOU SO MUCH!
@BritishTakeover for a tutor maybe, but public teachers are not making anywhere near that
The explanation you gave around 7:00 was exactly what I was searching for. Thank you very much
Thank you so so so soooo much!! 🙏 Ive been trying for 2 hours how to understand what I was doing wrong on my assignment on Khan Academy. The video that my teacher assigned for that assignment literally did not go over the different ways to solve the problems. But thanks to your “negative infinity & odd power = positive” & “negative infinity & even power = negative”, I finally understand how to do this! You did what Khan Academy could not, and for that I thank you from the bottom of my heart. Calculus is painful...
come back any time. these videos are made by someone who actually taught the material for many many years
exactly, Khan Academy too
: ) glad to have been of service!
People like you are why people are still succeeding in the bad school systems nowadays. Thank you
I was staring at that x^2 in the radical forever wondering how they got it in there if they divide by x. The book doesn't really explain it well. You explain in just minutes and bam! Thank you so much!
my calc teacher is soooo baddd at teaching omg + boring (she is obssessed with cows too)..weird a sshit...dude all i gotta say is that you have taught me what she tried teaching me over like 3 months..thank you so much and keep up the good work man...so glad there are people like you who are willing to give time for others you freaking rock!
This video is 12 years old but you just helped someone in 2020! Thank you so MUCH!
i don't know why everyone is so shocked :) the math does not change!
patrickJMT The math never changes, but the moment of elation that you get when everything makes sense is the greatest feeling of all! I was struggling with the negative sign on the odd powers for a good two hours, then I watched this video and it all made sense!
your prof is certainly correct. however, since we are doing x -->+infinity, the x value is already assumed to be positive, so we do not need to worry about +/- x... only +x
Patrick Thanks for these videos man. I've been watching them for the last two years to help me understand my pre-calc and calc. thanks alot man
i have a test tom. my prof has been trying to teach me this for the past 3 weeks. i'm learning it in 9 min... i love you....
@Kolbehh normally i get rid of the comments with profanity, but i will leave this one : )
Thank you! I was really confused about radicals in the denominator when the limit approaches negative infinity. My shitty calculus book has problems like this but doesn't explain how to approach them.
thanks alot, i have been sitting for hours and days trying to figure out things for my self with my 1000 page math book and long boring lectures without any result, but your videos really helped me to finaly understand it =D
@GoooboopTT come visit any time!
@ Lou, in this problem, square root of x^2 is indeed equal to x because we're being asked for the limit of the function WHEN x approaches positive infinity.
@MCNOVA21 my pleasure : )
@lucuador1992 no problem, come visit any time !
You are awesome. Also I love the way you start all of your videos with "ok..so.."
I wish all of my professors could explain thing so clearly.
@I3lak you were just lucky. you can not square the top and bottom of a fraction, in general, and have it be the same. think about 1/2 , for example.
This video was extremely helpful in helping me correct a mistake on a test I had. Thanks!
I watched the first example to find out how to do my assignment. I did all of the questions on it and then watched the rest of the video. turns out the second example was a question on my assignment and I had lost the negative sign in my work. thanks for the help!
You totally saved me from my first calc quiz. So glad that someone like you still exists in this world.lol Thanks a lot.
I basically only go to class now to get assignments.. I learn everything from your videos. Thanks so much!
its really interesting that whenever u write lim u put the dot of the i above m :L
how do you notice those things... :L
looool
I like that his radicals have a radical (end) edge better.
and yes, HOW do you notice these things, instead of the problems he's working for us, lmao....
I can no longer sleep at night
I stumbled upon this comment before watching the video and now ... oh dear.
my pleasure!
and... you live in austin too?!
gooooooooooooooooo austin!! moved here two years ago and totally love it, although the heat is starting to make me go insane i think...
Thank you so much. Today is our midterm exam and I finally understand the infinity limit. You've helped many people!!! Thank you may Godbless you.
Just thought you should know this video is WAY more helpful than the teaching process at school and Khan Academy’s demonstration of this topic. Thank you!!
glad i could help! come back any time
It would be awesome if you showed a problem that had a radical over the entire equation!
I figured it out tho watching this video...
thanks for all your vids Patrick, really helps me out!
Thanks for breaking down limits with radicals..our calc professor didn't touch on this but assigned problems with it!
If I don't understand a topic I d just have to go through your videos and somehow I ll just get it. Ure video tutorials does magic !!!
Thanks for explaining the sqrt(a) * sqrt(b) = sqrt(ab). I knew that rule, but didn't know I needed to use it to divide the radical by x. Turning x into sqrt(1/x^2). Was always wondering where the x^2 was coming from.
As other people have stated, since the sqrt of x^6 is abs x^3, you can determine that x^3 is negative when x approaches negative infinity in this video. That's how the negative 1 comes in
dude it is UNFATHOMABLE that 9 minutes of youtube beats an HOUR AND HALF of in class in my college. wtf, awesome.
Thanks so much, I saw the negative sign used in my notes and didn't understand it, this helped me so much!
thank you so much for your explanation of the negative sign at x approaching negative infinity! my teacher did not explain it well and i got really confused at first, but now after watching this it becomes so logical :)
Can you explain some more exercises about the limit of an absolute value? Thank you so much for your help.
Hi Patrick, what happens if numbers are raised to x power or x-root when x approaches infinity?
Example: 1) Limit 1^x as x->inf. How should we go about doing it?
2) Limit x->inf (2^x + 3^x + 5^x + 7^x + 11^x + 13^x)^(1/x)
thankkk youuu..ive been waiting to understand negative infinities for a longg timee..you are awsomee
Somebody give this guy an award, already. Patrick, you are the man!!!
From 2:06 on was the most enlightening thing I've seen this whole day. Of all things, math.
You are awesome! Such clear writing and very much to the point, all while explaining small rules that come with the limits of rational functions.
The second problem; 'x-> neg infinity with odd powers'. That was exactly what I was looking for, thanks for clearing up the issue.
different people are satisfied with different levels of work shown. you should ask your teacher / prof cause i really could not be sure
man you rock ... I really like your videos. They realllly help me a lot. I can't thank you enough :D
You are awesome! I had a similar question in my midterm as your second example, but I had no idea why there was a negative in the answer. You have cleared it up, just in time for my final exam upcoming in a week. Thanks for your videos!
Thank you for posting these videos. They are so helpful for studying.
I was wondering what you would do if the radical was on the numerator rather than the denominator?
Hallelujah finally I found something that tells me how to work with limit x going to neg infinity and radicals. Thank you!!
Man, i wish I could stuff you in my backpack and carry you around :(
You explain math so well...right now I'm in a class with a prof that's almost impossible to understand. I don't know how else I'd be learning calc on my own without youtube
how do you begin to think like that, the algebraic manipulation you did: 1/x^2 = squ(1/x^4) to get the two expressions under the same radical. I had a similar problem and I would have never fancied to do that.
that is incorrect algebra; you can not square the numerator and denominator and have it be equivalent (in general). 2/3 is not the same as 2^2/3^2 ; you are multiplying the numerator by 2 but the denominator by 3. this is a pretty common mistake though
Not what was done however
Wow, even though I'm kinda really late but this video saved me and I am really grateful. I'm really happy that I found the right video for my math problem, thanks!
How about radicals without a denominator such as sqrt(4x^2-2x+1)-2x as lim x->inf; multiplying by conjugate of 1 doesn't work, nor do normal methods. It evaluates to -1/2, but how can you solve it?
12 years ...am just watching it now 👏
This 12-year old video saved my day. Thanks man
Thank you so much for this!
My teacher was not helpful, and I just took what you had and expanded it to the square root of x^10 in the denominator.
@dinotles thanks : )
Best teacher......... u r the only math teacher i love 😊
i just asked the same question. There must be a reason, because when you graph this function, you see that it does tend to -1 as x goes to neg infinity. Id just like a less "hand wavey" explanation :) Even my professor could not really explain why. Perhaps because it is an odd function?. The numerator is x^3, which does produce the behavior that would require a negative limit.
You are very generous. Thank you so much for all of your videos.
well, you have to remember that you are taking a limit: the basic idea here is that if you put larger and larger values for x into the function (that is , as x --> infinity), the values of 4/x^2 and 3/x will get arbitrarily close to zero.
Wow, that negative infinity sum is awesome. thanks for the video. Your teaching is awesome.
I was wondering...
What do you do if the radical is in the numerator? Do you use the same method?
@patrickJMT lmao!!!! omg i just wanted to tell you thank you for taking time out to do these videos. I swear i was failing this class an i'm determined to get an A. Thank yous soo much. Idk if u know how much it means to me, cause i suck @ math :(
yes, you choose the highest power in the denominator.
What about if the degree under the radical was odd? You only gave examples of it when it was even. Do you still do the same thing except divide by the degree over two (because of the square root) times the radical x?
ex. denominator = sqrt(x^3 + 7) would you divide by x*sqrt(x)?
6:58, if we have to use negative sign for 1/x^3 in denominator, why not for numerator??
think about what would happen to those expressions as you take the limit...
You have helped me so much in calculus you are a life saver!!! :)
Just amazing! I was struggling with the negative infinity in limits and you explained it crystal clear!
so on the second problem when the limit with x going to the -infnity, if I hadn't put the negative sign before the root of 1/x*6, that would be false?
@patrickJMT But at 8:38 , Couldn't sqrt(1) be equal to +1 or -1?
Gautham Shankar no because u are taking a limit of a function
So it will just be +1
is there a certain rule to it? i too always thought it could be postive or negtive and im confused rn
I cant believe this video was made 12 yrs ago. I was like jinjja? 😲 Anyways 'til now this helps me a lot. Especially this time of crisis where we're having online class. We have to teach ourselves. 😔😔 Thank you really! This might save me from my exam next week ♡♡♡
@ThundaSundaa you do the exact same thing
Your videos are more helpful than my lectures!! Thank-you so much for the examples!
Since x approaches negative infinity (x
How do you do one like this:
Limit as x approaches 1 of (x^(1/3)-1)/(x^(1/4)-1)
I love how I find this really helpful in 2020. 12 years later from today's video !!!
people really are fixated on how old this videos are :)
I have been watching your videos for 4 years now :) Thank you! much more helpful than kahn academy :)
My question. in your second example, you show that (1/x^2)^1/2 = 1/x, and because the limit goes to neg infinity, we tack on a -, such that -(1/x^2)^1/2 = -(1/x). Wouldn't the same then be true for the numerator? -(1/x^2)*x^2 would yield -1 in the numerator, and then -1 in the denominator, resulting in the limit being 1, and not -1? Why do we only tack the neg sign in the denominator?
in the second question ,you divided the numerator with x^3. were you not supposed to divide it with -x^3 just like you divided in the denominator with -x^3 since the limit is going to negative infinity and also that the power isn't even?
Thanks! You cleared up the negative-infinity problem for me.
oh You're making me fall in love with math all over again! Thanks a bunch!
Fantastic video! Except, I'm a little confused at 5:37 when you found that the square root of 1/x^6 is the same as 1/x^3. Why is that? I would have thought it would be 1/x^9 because the square root of 9 is 3. Could you explain this please?
12 years later, this video helped me out to prepare for the midterm tomorrow! Thanks!
i made it just for you!
Do you put the negative sign on the top also or just on the bottom?
do you always get the highest power from the denominator or from wherever the radical is preset? (Numerator or denominator)
sorry about the double comments, my internet was acting up.
I also wanted to know what do you do if the radical is like the sqrt( 9x^2 + 4). Do you keep the 9 and take the root of it?
dude I literally dominate math courses because of you.
Why do u first need to turn the thing you are dividing by in the denominator into a radical before you think about what would happen the limit as approaches negative or positive infinity
is it wrong if i square both numerator and denominator to get red of the radical sign? this did work with the first example but it did not with second one. i don't know why?
You are the best.
This is exactly what I was looking for!
Thank you!
I'm assuming that if the highest powered x came with a number like 9x^2, I would divide all by 3x? or is it still just x?
@patrickJMT Well, that shows how humble you are(:- You're my role model and hero. Really, when I grow up I wanna be just like YOU! Go patrickJMT!
for the second example, couldn't you technically say that the degree of the numerator (which is x^3) and denominator (which is x^(6/2)=x^3) are equal, thus the limit would equal the ratio of the coefficients of those terms which would be 1/1 = 1? but the solution should apparently be -1. i'm just a little confused on why that rational function trick doesn't work for example 2. thanks so much for all your help! your videos are awesome
Well since you're approaching negative infinity, that is how the trick would result in -1 I believe.
...I am answering 8 months later, so I'm wondering if this advice is still applicable haha