Algebra - Free Formula Sheets: bit.ly/3CBeZMY Final Exams and Video Playlists: www.video-tutor.net/ Next Video: th-cam.com/video/bWVhwYdSnfk/w-d-xo.html
When you have a gift it can seem wild to those who don’t share the same gift, he probably understands saying or teaching something that may seem complex to many that the best way is to try to make it sound as simple as possible and it seems that he loves teaching.
was gonna say i didn’t understand the long division part then i watched his video explaining how to do them and now this video is so easy to understand. guy’s a genius
very late reply but there is a quicker way called synthetic division, when you're dividing by those trinomials with a binomial it makes it so much easier.
in the first case of slant asymptote the asymptote does not exist since the remainder of long division is zero and if we cancel out the terms we see that we get linear function with equation y = x + 2 with a missing point at x = -3 which lies on the asymptote and that contradicts with the definition of an asymptote
tenure this is when school sign contracts with teacher pretty much guarantees them a job for life no matter what. That's why when you get a bad teacher most of the time they get away with it. Even if they are so bad and the school decides to fire them the school has to go through a complicated process that can last at least a year or longer. Chances of a teacher getting fired is 1 in 2000 compared to a doctor which is 1 in 57. The American public school system sucks. We need more teachers like this dude.
I have a teacher for calculus 1 that hasn't taught for 14 years and came back and she is terrible at teaching she goes on the textbook says copy down this example (explains nothing) then says to do questions 1-4 without telling us how to do it so every class we have to learn it on our own
its easy to remember if u think like this... Think the rational expression as a building if its top heavy just by one it will collapse but not desintagrate resulting in a oblique line if its top heavy by more than one it will collapse and desintagrate, theres no line! if its bottom heavy well the building its on the floor as it should be, y=0 if top and bottom are equally heavy, then divide those bad boys
*Why do bad teachers get paid?:* tenure this is when school sign contracts with teacher pretty much guarantees them a job for life no matter what. That's why when you get a bad teacher most of the time they get away with it. Even if they are so bad and the school decides to fire them the school has to go through a complicated process that can last at least a year or longer. Chances of a teacher getting fired is 1 in 2000 compared to a doctor which is 1 in 57. The American public school system sucks. We need more teachers like this dude.
I'm talking about: x^2+5x+6/X+3, but algebraic long division is probably something to get marks in the exam, rather than factoring, both ways are not that hard, after you explained them.
Sorry, how can there be a slant asymptote if the equation at 5:20 factors cleanly into [x+2] without a remainder? Shouldn't there be a slant asymptote only if it leaves a remainder?
I hv exam of calculus on 21 dec, well this sir is gonna help me so much, u teach so well , i only have watched 2videos of yours and i feel like i will pass onlye because of you sir ,thank you 🤞✨
So, there is a major maths error in this video. Starting at 5:00 We are given the equation: (x² + 5x + 6) y = --------------------- (x + 3) which, when properly factored, is: (x + 2)(x + 3) y = ----------------------- (x + 3) So, even though the numerator is 1 degree larger than the denominator, it also shares a common factor with the denominator of (x + 3). Before dealing with asymptotes, we have to remove any *holes* that may be present in the graph, and this matching (x + 3) factor tells us that there is actually a HOLE at x = -3, not a slant asymptote. Removing this hole from our equation gives us our actual graph which is now reduced to just the graph of: y = (x +2) with y's domain restricted to all real numbers *except* x = -3 that is, our function is simply: y = x + 2 Domain: (-∞, -3) ∪ (-3, ∞) Plug this into a graphing calculator if you want to double check - the graph is just a straight line that is undefined at x = -3 You can't have an oblique asymptote if your graph itself is just a line
Y=(x²-3x+4)/(x²-6x+8) Y=1 is the horizontal asymptote but when you graph it it is only applicable on the right side of the graph but when you extend the line y=1 to the left it will intersect the graph of the given rational equation.
OMG! I thought I was the only one losing my mind over here. I'm *fairly* certain, this would be a line with a hole. This dude now has me scouring the internet in search of my sanity.
The other oblique asymptote is good, but I think it's best to write out the full answer (kind of like a mixed number). The rational function, after long division, equals 2x + (-16x+6)/(xx+4). Then analyze as x approaches infinity....(-16x+6)/(xx+4) will approach zero....ie leaving y=2x as the oblique asymptote.
THANK YOU 💚👀✨ I didn't understand how to find Slant asymptote, but I'll understand I watched this video twice, and now I better understand how to find slant asymptote :з)
Im confused about if these rules ALWAYS apply. For instance take (5x + 1) / (x^2 - x - 1) and graph it in the graphing calculator. There appears to be a horizontal asymptote at y = 0. However there is a vertical like that strikes through y = 0 in between 2 other lines in the function. Does the horizontal asymptote still apply?? Do these set of rules apply no matter what? If anyone could help that would be wonderful!! Thank you
is there a way to rationally calculate these without knowing any tricks like "If the degree is the same devide the coefficients". I want to know how to look at a function and see in my head where the asymptotes would be
7:54 I wish my teacher taught us this before the quiz. I was freaking out because of the remainder since the mulitple choice answer didn't contain the remainder.
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Algebra - Free Formula Sheets: bit.ly/3CBeZMY
Final Exams and Video Playlists: www.video-tutor.net/
Next Video: th-cam.com/video/bWVhwYdSnfk/w-d-xo.html
Thank you
Why does this guy make things look so much more easier than my teacher does, your actually going to help me pass my precalculas class
My teacher is doing this in algebra 2 😸
@@nightandday7704 the go over it in pre-calc too
When you have a gift it can seem wild to those who don’t share the same gift, he probably understands saying or teaching something that may seem complex to many that the best way is to try to make it sound as simple as possible and it seems that he loves teaching.
I’m in the same exact situation lmao
literally i’m in this exact position
There’s a special place in heaven for you
Amen! 🙏😇
Amen
I hope i meet him if i get in heaven
@@BoonkiCoC14 XD yeah if I get into heaven
Yes lawd
He's always so calm in every single video. Just peaceful teaching. And he breaks everything down so well.
I wish every teacher in the world would teach like you do.
was gonna say i didn’t understand the long division part then i watched his video explaining how to do them and now this video is so easy to understand. guy’s a genius
very late reply but there is a quicker way called synthetic division, when you're dividing by those trinomials with a binomial it makes it so much easier.
you're the reason why I'm starting to love math☀️
I have a national exam in 2 months and you've relieved a lot of stress for me. Thank you so much. God bless you!!!
GOOD LUCK DUDE !!!
@@cecilion4909 tnxs
@@metiguda473how’d it go?
MR. Organic Chemistry tutor ,thank you for a well explained and solid analysis of Horizontal and Slant Asymptotes in precalculus.
You explained what my teacher couldn’t answer in less than 5 seconds. I love you
You’re the reason I’m going to pass this math class 🙌
in the first case of slant asymptote the asymptote does not exist since the remainder of long division is zero and if we cancel out the terms we see that we get linear function with equation y = x + 2 with a missing point at x = -3 which lies on the asymptote and that contradicts with the definition of an asymptote
exactly i was confused on why he said it was slant
I swear your the best math channel I have ever seen been helping me for years
Why do teachers get paid when I don’t even learn from them.
Question of the century
tenure this is when school sign contracts with teacher pretty much guarantees them a job for life no matter what. That's why when you get a bad teacher most of the time they get away with it. Even if they are so bad and the school decides to fire them the school has to go through a complicated process that can last at least a year or longer. Chances of a teacher getting fired is 1 in 2000 compared to a doctor which is 1 in 57. The American public school system sucks. We need more teachers like this dude.
I have a teacher for calculus 1 that hasn't taught for 14 years and came back and she is terrible at teaching she goes on the textbook says copy down this example (explains nothing) then says to do questions 1-4 without telling us how to do it so every class we have to learn it on our own
I should thank you my friend. I learned a lot from your great videos. They are very easy and fast to understand and learn. Tnx a lot
By a student from hk: your video is really useful that you make a student from the other side of the world to understand, thanks a lot
its easy to remember if u think like this...
Think the rational expression as a building
if its top heavy just by one it will collapse but not desintagrate resulting in a oblique line
if its top heavy by more than one it will collapse and desintagrate, theres no line!
if its bottom heavy well the building its on the floor as it should be, y=0
if top and bottom are equally heavy, then divide those bad boys
omg... this is genius thank you
This is actually so smart thanks!
This man is legendary.
Damn this guy just taught me all the knowledge my teacher has been teaching us for weeks that I haven’t understood until now
The only teacher who literally use a BLACKBOARD thank youuu you helped me a lot 😭❤️
super expensive college textbooks are pretty much useless when free youtube is here. thank you.
Here 30 minutes before my exam just for a recap! Always a lifesaver 💛
thank you, TheOrganicChemistryTutor for making my and millions of others lives easier when it comes to our studies.
I will protect you at all costs, thank you for getting me through class
By the way, synthetic division can be used to find the asymptote, although it might be easier to use polynomial long division in certain situations.
Is synthetic devision the same as long division?
@@daniaalsadi7208 you end up getting the same answer in both but the way you get that answer is little different.
imo synthetic division is more convenient to use
I'm writing my second Calculus test on Thursday, and I'm confident I'm also gonna pass it. Thank you for your existence❤️
its amazing how you didnt stretch this into an 80 minute lesson for absolutely no reason!
This is the guy graduating me from uni. Thank you sir😊😊
8:28 but that one has an asymptote where it's a cubic function
GOOD WORK MAN..
İ honestly wish your videos had ads in my country so i could watch the entire ad without skipping as a form of appreciation
this dude is the only real math teacher
*Why do bad teachers get paid?:* tenure this is when school sign contracts with teacher pretty much guarantees them a job for life no matter what. That's why when you get a bad teacher most of the time they get away with it. Even if they are so bad and the school decides to fire them the school has to go through a complicated process that can last at least a year or longer. Chances of a teacher getting fired is 1 in 2000 compared to a doctor which is 1 in 57. The American public school system sucks. We need more teachers like this dude.
I recommend watching waiting for superman if any of you are interested on this topic. It's currently on Netflix. Or just look up the facts
😊 thanks for being the best math teacher I had ever come across
Comment for engagement
You’re better than my college professor
Appreciate it homie
You have delivered real knowledge... that too with such ease.. great. Thanks!
10:01 lmao i thought it was (7x-y) + y but the y was actually 4 😂 anyways great video man!
Absolute CHAD! TYSM!
I'm talking about: x^2+5x+6/X+3, but algebraic long division is probably something to get marks in the exam, rather than factoring, both ways are not that hard, after you explained them.
God bless this man, I hope nothing but the best for him genuinely.
Sorry, how can there be a slant asymptote if the equation at 5:20 factors cleanly into [x+2] without a remainder? Shouldn't there be a slant asymptote only if it leaves a remainder?
yes i think youre right, he made a mistake
This man is saving me in precalc
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I hv exam of calculus on 21 dec, well this sir is gonna help me so much, u teach so well , i only have watched 2videos of yours and i feel like i will pass onlye because of you sir ,thank you 🤞✨
Yes the videos from 2006 are really helping
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Organic chemistry teacher my beloved
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So, there is a major maths error in this video.
Starting at 5:00
We are given the equation:
(x² + 5x + 6)
y = ---------------------
(x + 3)
which, when properly factored, is:
(x + 2)(x + 3)
y = -----------------------
(x + 3)
So, even though the numerator is 1 degree larger than the denominator, it also shares a common factor with the denominator of (x + 3).
Before dealing with asymptotes, we have to remove any *holes* that may be present in the graph, and this matching (x + 3) factor tells us that there is actually a HOLE at x = -3, not a slant asymptote.
Removing this hole from our equation gives us our actual graph which is now reduced to just the graph of:
y = (x +2)
with y's domain restricted to all real numbers *except* x = -3
that is, our function is simply:
y = x + 2
Domain: (-∞, -3) ∪ (-3, ∞)
Plug this into a graphing calculator if you want to double check - the graph is just a straight line that is undefined at x = -3
You can't have an oblique asymptote if your graph itself is just a line
Bro you rock!Jesus bless you!
Exactly what I was looking for!
You teach this way better than my math teacher😂
You came through brother! Thanks!
he was sick or something?
I learned more from the first 50 seconds of this video than I did from my actual textbook
you deserve a cookie
Omg you helped me so much many blessings to you
thank you may God bless you more
Y=(x²-3x+4)/(x²-6x+8)
Y=1 is the horizontal asymptote but when you graph it it is only applicable on the right side of the graph but when you extend the line y=1 to the left it will intersect the graph of the given rational equation.
I really fucking love man, you have no idea how much help and hope you give people like me!
I wish we learnED this!
You're just the best ❤❤❤❤❤❤❤❤❤❤❤
4:00 - isn't this just equivalent to x+2, a linear function with no asymptotes?
OMG! I thought I was the only one losing my mind over here. I'm *fairly* certain, this would be a line with a hole. This dude now has me scouring the internet in search of my sanity.
i’m literally in love with you
Really useful, thank you so much!
The other oblique asymptote is good, but I think it's best to write out the full answer (kind of like a mixed number). The rational function, after long division, equals 2x + (-16x+6)/(xx+4).
Then analyze as x approaches infinity....(-16x+6)/(xx+4) will approach zero....ie leaving y=2x as the oblique asymptote.
Great lessons sir, I learn a lot of you ! Thank you very mutch
I will send this video to my teacher so that he learns from you, you are a master at teaching, he tries to make it 10x harder than it is
My appreciation sir❤
THANK YOU 💚👀✨ I didn't understand how to find Slant asymptote, but I'll understand
I watched this video twice, and now I better understand how to find slant asymptote :з)
I SWEAR TO GOD YOU ARE GETTING ME THROUGH COLLGE!!!!
Im confused about if these rules ALWAYS apply. For instance take (5x + 1) / (x^2 - x - 1) and graph it in the graphing calculator. There appears to be a horizontal asymptote at y = 0. However there is a vertical like that strikes through y = 0 in between 2 other lines in the function. Does the horizontal asymptote still apply?? Do these set of rules apply no matter what? If anyone could help that would be wonderful!! Thank you
Amazing sir❤
Very good explanation.
is there a way to rationally calculate these without knowing any tricks like "If the degree is the same devide the coefficients".
I want to know how to look at a function and see in my head where the asymptotes would be
Thanks a lot bro. Your videos helping so well 👍🏻
You made me temporarily like math. Thank you lol
The best right here for a fact
I have a final exam after 53 mins ... thank you for saving me 😂🤝🏼
you literally saved me a week of pain
This guy teaches more of this lesson than my teacher does 💀
You are a legend
7:54 I wish my teacher taught us this before the quiz. I was freaking out because of the remainder since the mulitple choice answer didn't contain the remainder.
U are lucky u hv multiple choice
Amazing explain...