Limits at Infinity & Horizontal Asymptotes

This calculus video tutorial explains how to evaluate limits at infinity and how it relates to the horizontal asymptote of a function. Examples include rational functions, radical functions, inverse trigonometric functions and exponential functions. This video contains plenty of practice problems on evaluating limits at infinity analytically with radicals, square roots, and trig functions.
Introduction to Limits:
• Calculus 1 - Introduct...
How To Evaluate Limits From a Graph:
• How To Evaluate Limits...
Evaluating Limits By Factoring:
• Evaluating Limits By F...
Limits of Rational Functions :
• Limits of Rational Fun...
Limits of Radical Functions:
• How To Evaluate Limits...
Limits of Trigonometric Functions:
• Limits of Trigonometri...
___________________________________
How To Find The Limit at Infinity:
• How To Find The Limit ...
Infinite Limits + Vertical Asymptotes:
• Infinite Limits and Ve...
Limits at Infinity With Radicals:
• Limits at Infinity Wit...
Limits of Absolute Value Functions:
• Limits and Absolute Value
Limits of Composite Functions:
• How To Find The Limit ...
The Squeeze Theorem:
• Squeeze Theorem
____________________________________
Limits and Logarithms:
• Limits and Logarithms
Limits of Exponential Functions:
• Limits of Exponential ...
Piecewise Functions - Limits:
• Piecewise Functions - ...
3 Step Continuity Test:
• 3 Step Continuity Test...
Continuity and Differentiability:
• Continuity and Differe...
Limits - Test Review:
• One Sided Limits, Grap...
_____________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 306

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor Жыл бұрын

    Final Exams and Video Playlists: www.video-tutor.net/ Math and Science Tutors: bit.ly/Find-a-Tutor Next Video: kzread.info/dash/bejne/mHyuz7Omk9nOlaw.html

  • @inemibok

    @inemibok

    Жыл бұрын

    Can someone please explain why at 10:13 he multiplied both top and bottom by 1/x instead of 1/x² @The Organic Chemistry Tutor Tnx ❤️

  • @adamantcapitol
    @adamantcapitol Жыл бұрын

    Your explanations are simply the best. I appreciate so much that you don't take shortcuts and aren't afraid to review the fundamentals during the examples. I wish I could pay you for my Calculus class instead of my university.

  • @HarvardUni

    @HarvardUni

    5 ай бұрын

    AGREED

  • @o.g.dominus
    @o.g.dominus3 жыл бұрын

    Fun fact: Everybody rushes down here when a test threatens them. Don't worry, we are all in this together. I have a test by sunrise.

  • @fazalshaik8399

    @fazalshaik8399

    3 жыл бұрын

    Same

  • @fazalshaik8399

    @fazalshaik8399

    3 жыл бұрын

    How did it go??

  • @o.g.dominus

    @o.g.dominus

    3 жыл бұрын

    @@fazalshaik8399 To summarise it, I just scored a 5.0/5.0 in my math this semester. Thanks to this tutor here

  • @fazalshaik8399

    @fazalshaik8399

    3 жыл бұрын

    @@o.g.dominus I hope mine does too

  • @o.g.dominus

    @o.g.dominus

    3 жыл бұрын

    @@fazalshaik8399 Good luck brother. I pray you get it too🙏

  • @splendidjihoon5464
    @splendidjihoon54645 жыл бұрын

    i wasted my 3 hrs listening to my calculus teacher without learning it. and now, i learned it instant for only 20 min. wow. thanks

  • @pandavx

    @pandavx

    3 жыл бұрын

    x2 the speed and learn it in 10 min

  • @alikhidzam3749

    @alikhidzam3749

    3 жыл бұрын

    My calculus teacher dint even teach how to find the limit of infinity

  • @diglis1033

    @diglis1033

    2 жыл бұрын

    @@alikhidzam3749 you serious? That should be one of the first things you learn in calc 1

  • @afrolly2215
    @afrolly22155 жыл бұрын

    You’re a life saver man I love your videos, you explain better than my college professor lol

  • @munenebrilliant1774
    @munenebrilliant17746 жыл бұрын

    God is using you man .

  • @gyroxaver6897

    @gyroxaver6897

    4 жыл бұрын

    That's a Factoid

  • @lillian5353

    @lillian5353

    4 жыл бұрын

    For brighter and better things

  • @jailkhan8548
    @jailkhan85482 жыл бұрын

    In 20 mins i have learned more than I ever did from my prof's lectures.

  • @omarahmad2311
    @omarahmad23112 жыл бұрын

    My prof is a German teacher with the heaviest accent ever, I also don’t really understand her method, but this one man explains in one clear shot 💯

  • @mohamedkhaled1150

    @mohamedkhaled1150

    2 жыл бұрын

    isabelle in auc ?

  • @y2ksteppa

    @y2ksteppa

    3 ай бұрын

    @@mohamedkhaled1150 i think so

  • @georgesadler7830
    @georgesadler7830 Жыл бұрын

    MR. Organic Chemistry Tutor, thank you for an excellent explanation of Limits at Infinity and Horizontal Asymptote in Calculus One/Two.

  • @Mayoda4real
    @Mayoda4real2 жыл бұрын

    This man just proves how bad, some university teachers are, they are paid a bunch of money but can't teach shit. This man makes it so simple to understand. Thanks for this channel

  • @blaq-barbieandnick497
    @blaq-barbieandnick4972 жыл бұрын

    why do we have to multiply the fraction by 1/x😢

  • @user-tw4kt8du9t
    @user-tw4kt8du9t4 жыл бұрын

    I actually dont know how many extra hours I would spend on calc without your videos. Thanks so much. Youre a god.

  • @youssefosama4466
    @youssefosama44666 жыл бұрын

    Keep it up man,you're a huge help

  • @TheOrganicChemistryTutor

    @TheOrganicChemistryTutor

    6 жыл бұрын

    Thanks

  • @iiii1450
    @iiii14505 жыл бұрын

    you are really really really helping me in physics and also calculus, man you are really better than all the professors in my university you are a great teacher i am really rely on you man thank you soooooo much

  • @garangbol793

    @garangbol793

    4 жыл бұрын

    أخيراً في واحد عربي

  • @m7mdarwani964

    @m7mdarwani964

    4 жыл бұрын

    @@garangbol793 في كثير عرب معتمدين على الله ثم على هالشب

  • @williamessel2958
    @williamessel2958 Жыл бұрын

    Notice that he never asks you to subscribe😂😂😂. Legendary

  • @user-np7nk3cj3v

    @user-np7nk3cj3v

    Ай бұрын

    Coz he knows you'll be watching his videos when exams arrive 😂😂😂

  • @user-np7nk3cj3v

    @user-np7nk3cj3v

    Ай бұрын

    Coz he knows you'll be watching his videos when exams arrive 😂😂😂

  • @samiulislamdurjoy
    @samiulislamdurjoy3 жыл бұрын

    G 191 11:38 note 5:25 any time the function is bottom heavy with infinity limits the functions is equal to zero note 5:25 any time degree is equal the ans is coefficient ratio

  • @nicholasachuz8329
    @nicholasachuz83292 жыл бұрын

    This was helpful as always, yet it is still challenging to me a little bit because there's no consistency in the procedures so that we can use the same approach to every rational function.

  • @hanslarrobis117
    @hanslarrobis1172 жыл бұрын

    may i ask on the second to the last problem, why do we need to multiply 1/x on both sides?

  • @5nanometers
    @5nanometers10 ай бұрын

    16:14 Why did he multiply the radical in the denominator by 1/x^2, but the rest of the denominator by 1/x? I'm guessing it's because in the end, you're taking the limits individually, but I don't get the rule

  • @mirana6157

    @mirana6157

    4 ай бұрын

    "Inside a radicle, we need to multiply by 1/x^2" is what he says. Because the 1/x is going under the radicle, its supposed to turn into 1/x^2. Hope this helps!

  • @michellecampa9850
    @michellecampa98502 жыл бұрын

    at 16:06 shouldntthe 9 be multiplied by 1/x^2 instead of 1/x because x^2/x is still x???? im confused pls help

  • @plon5284

    @plon5284

    Жыл бұрын

    ok im a year late but it turns out to be 9 because to be able to multiply √(9x^2) by (1/x) to cancel out the highest exponent, you need to get into the radical. So what he did without explaining was he converted (1/x) into (1/√x^2) bc they're the same, so √(9x^2)/(1/x) = √(9x^2)/√(1/x^2) which makes it √9. -bored college student

  • @HAHA-rf4dc
    @HAHA-rf4dc3 жыл бұрын

    every time when i fell hopeless for math, you came out

  • @MaurianeBanza
    @MaurianeBanza Жыл бұрын

    I understand Math with you better than my prof. Your voice helps me

  • @GivenNgomane-ue9uv

    @GivenNgomane-ue9uv

    3 ай бұрын

    ditto, like same

  • @shuhadakherudin5468
    @shuhadakherudin54683 жыл бұрын

    watched your vids for my igcse revision. I'm in college now and I still watch your vids to understand better. Thank you!

  • @carolnoelle2468
    @carolnoelle246814 күн бұрын

    The x doubles inside the sqr rt! Omg thank goodness I was so confused thanks!!!!

  • @maryam4587
    @maryam45874 жыл бұрын

    "The exponent doubles once you move it inside" 19: 21 I bet many of you are confused but hopefully this one sentence help just like it helped me lol

  • @sharansahota5498

    @sharansahota5498

    4 жыл бұрын

    thank youuuu I was confused on that

  • @kofi4927

    @kofi4927

    3 жыл бұрын

    bruh i was hella confused about this before i saw this video

  • @unknown159
    @unknown159 Жыл бұрын

    I am here before every test, this time I am here before my final. Somehow just from watching these videos for like 2 days, I manage to always ace my tests, even though I slacked off the entire semester. LOL

  • @darthTwin6
    @darthTwin6 Жыл бұрын

    Very Helpful For My AP Calculus BC class. You're a lifesaver!

  • @ish1mwe
    @ish1mwe Жыл бұрын

    Good professor, I wish you to come in Rwanda🇷🇼 C's we love you alot. God bless you.

  • @frankchitala1164
    @frankchitala116411 ай бұрын

    well articulated and i could go on and work out on the rest of the questions on my own. 🙏

  • @supernova9752
    @supernova975210 ай бұрын

    thank you so much, you're saving my calculus grade and i'm actually learning and understanding what to do

  • @daneshipway581
    @daneshipway5813 жыл бұрын

    Mate I love your videos, I've been writing out the theory understanding as best I can and as soon as I hit a road block your the man I come to, and everything I've learnt makes fence

  • @sofzhuk1188
    @sofzhuk11883 жыл бұрын

    first calc test tomorrow and I think you'll be the reason I pass :) thank you

  • @cloudslady3400
    @cloudslady34003 ай бұрын

    The best thing about this guy is how short his videos are I spent days and days studying with zero results…in less than twenty minutes it all makes sense

  • @juevee4341
    @juevee43414 жыл бұрын

    can i know how to solve the question at @14.35 if the limit is at negative infinity

  • @elis2506
    @elis25063 жыл бұрын

    quick question, for the problem w (square root of 9x^2+x) - 3x, why couldnt we plug in infinity right away? x^2 is the biggest term, so wouldn't it determine the behavior of the limit and cause it to tend towards infinity?

  • @mmatlouchristainah4947
    @mmatlouchristainah49474 жыл бұрын

    Ur video's are the best 💯 thank you for helping me 🙏

  • @suverchasharma1814
    @suverchasharma18143 жыл бұрын

    Thank you so much, the wide range of examples really helped me out!

  • @jazzm786
    @jazzm786 Жыл бұрын

    this is suchhh a good explanation. i needed this step by step explanation

  • @tranquoclan5043
    @tranquoclan50433 жыл бұрын

    At 11:35, since x goes to infinity, I think that we have to consider both case: (1) x goes to positive infinity and (2) x goes to negative infinity. In case (1), the answer is 2 (positive 2), but in case (2) the answer is -2 (negative 2) . In this problem, the method divide both numerator and denominator by 1/x is not a good choice. Instead, divide both numerator and denominator by 1/abs(x) (abs(x): absolute value of x) would be more generally correct. In case (1), 1/abs(x) equals 1/x (positive 1/x) and in case (2), 1/abs(x) = 1/-x (negative 1/x).

  • @SenumiDinanga
    @SenumiDinanga3 жыл бұрын

    Thank you soo much for putting out these vids! legit I'm so grateful! you literally make me love maths

  • @madhuradeshmane9612
    @madhuradeshmane9612 Жыл бұрын

    thank you ,learned a lot in this video and you are a huge help

  • @AsifRaf1
    @AsifRaf12 жыл бұрын

    Best maths teacher Thanks a lot for all the help

  • @daniellakayedolotalias3326
    @daniellakayedolotalias33268 ай бұрын

    Your videos really are a big help to me. Thank You!

  • @edelwafula378
    @edelwafula3782 жыл бұрын

    Thank you very much at least you have given me directions and I would like you to give us as more examples as possible for me to be in a good position..

  • @Bilalsahmad
    @Bilalsahmad2 жыл бұрын

    i have my test tommorow and you saved my life, thanks

  • @gregsong1388
    @gregsong13883 жыл бұрын

    literally SAVED my life.

  • @okekeemmanuelchidubem9807
    @okekeemmanuelchidubem98074 жыл бұрын

    this tutorial is really helpful to me

  • @nanayawksiriboe7426
    @nanayawksiriboe74263 жыл бұрын

    what would be a genral equation to write for the definition of vertical and horizontal asymptotes using limits.

  • @jonnydobandliamried8094
    @jonnydobandliamried80945 жыл бұрын

    THANK U, some other vid just showed dthe tricks on how to figure it out but didn't explain y, thanks man

  • @yapsejaiteh7
    @yapsejaiteh73 жыл бұрын

    Your explanation are really clear and understandable. Your videos are really helping me

  • @asoup1972
    @asoup1972 Жыл бұрын

    The answer at 9:20 really helped me out. Thanks a lot!

  • @kurokubushi
    @kurokubushi8 ай бұрын

    One short cut rule you didn't seem to cover was when the x value is greater in the numerator (ex: 3x^4-10/6x^2+20) the limit will be +/- infinity since the top is outgrowing the bottom.

  • @ajibolabalogun9834
    @ajibolabalogun9834 Жыл бұрын

    In 11:51 why are we multiplying by 1/x³ instead of 1/x since this question is bottom heavy? Does anyone know?

  • @simonpeapo9521
    @simonpeapo95213 жыл бұрын

    King 👑 of maths,, gifted mind

  • @justinfisher5339
    @justinfisher53393 жыл бұрын

    This is the insanely interesting actually.

  • @sarafeliciano3088
    @sarafeliciano30883 жыл бұрын

    Amazing video! Cheers!!

  • @rowanschelvis4305
    @rowanschelvis43055 жыл бұрын

    Great video, very helpfull

  • @crispychickenwing
    @crispychickenwing4 жыл бұрын

    @ 12:54 why did the sign change from - to +?

  • @dagatejohnelo.6153
    @dagatejohnelo.61532 жыл бұрын

    Thank your so much ,I really struggling to this

  • @muthoninthiga
    @muthoninthiga Жыл бұрын

    Thanks so much, this is so helpful

  • @sokham4523
    @sokham45232 жыл бұрын

    hi, what is the answer if infinity of a limit of n^2/2^n?

  • @delulus_0
    @delulus_0 Жыл бұрын

    15:36 why did he multiply the top and the bottom with 1/x instead of 1/x^2 since the highest degree is 2?

  • @DanielKuvanychbekov

    @DanielKuvanychbekov

    4 ай бұрын

    same question

  • @kennethjoseph8360
    @kennethjoseph83602 жыл бұрын

    Am naming my first born after you 🤌🏾🙌🏾

  • @ralphpagangpang9390
    @ralphpagangpang93903 жыл бұрын

    Kudos to this guy u really save me in my online class frustration

  • @priyaangadi1213
    @priyaangadi1213 Жыл бұрын

    awesome math tutorial .

  • @VeritasEtAequitas
    @VeritasEtAequitas4 жыл бұрын

    Can you.please show these carrying the proper Lim notation through the whole problem? Even with the "work" shown, it skips steps or notation which we need to show on every step.

  • @noelkuhomiemaihi5542
    @noelkuhomiemaihi55424 ай бұрын

    Thank you so much Mr Julius Gonzalex

  • @wentaeeeee7957
    @wentaeeeee79572 жыл бұрын

    do u have limit at infinity with table of values??

  • @clinediamond123
    @clinediamond1233 жыл бұрын

    thank you so much for this!!!!

  • @ClooverDevs
    @ClooverDevs Жыл бұрын

    u have the most positive effect on this humanity only god knows how to reward u..... class of 2023 appreciates u 🙏🙏🙏

  • @Cat-ij2rk
    @Cat-ij2rk2 жыл бұрын

    Honestly, Thank you so much!

  • @nawafalmatruk297
    @nawafalmatruk2975 жыл бұрын

    thank you so much sir

  • @nickareekadan7313
    @nickareekadan73134 жыл бұрын

    hey at 12:56 why did the square root of 1/x^6 (9x^6 - x^2) turn into square root (9 + ....) which is addition now? where did the addition sign come from??

  • @johnleandrepermison7175

    @johnleandrepermison7175

    5 ай бұрын

    Same question right here too😂😅

  • @hooligan1602
    @hooligan16025 ай бұрын

    I haven’t finished the video but I’ve been studying other calc sections for my quiz tomorrow and you just apply the power rule to top and bottom and you get the answer, so all constants = 0, for the constants that have a variable you multiply it by 1 and divide and get the answer. hopefully this helps someone in the future!

  • @graceful522
    @graceful5223 жыл бұрын

    what about when the numerator has a higher degree? I learned in stats that there would be no HA, but in calc its telling me the answer should be infinity and idk why

  • @doaaahmed9730
    @doaaahmed97305 жыл бұрын

    Thanks a lot 😊😊... Your videos help me a lot in my college 👌👌 Greetings from Egypt 🇪🇬 ✌️

  • @davidkeele5056
    @davidkeele50562 жыл бұрын

    This was so unbelievably helpful thank you

  • @Melinda-xx8oe
    @Melinda-xx8oe5 жыл бұрын

    The best freaking video on KZread

  • @Isra003
    @Isra0032 жыл бұрын

    I want to ask something ( plz answer i have an exam ☹) ... At 9:39 how can I make sure that the value of X is so big that I can ignore the other values?

  • @joshuasangabriel1088
    @joshuasangabriel10886 жыл бұрын

    Thanks bro..

  • @janettemireles6731
    @janettemireles67314 жыл бұрын

    isn't 9x^2 times 1/x = 9x, not 9? @ 15:54

  • @edwardgilbert5803

    @edwardgilbert5803

    4 жыл бұрын

    thats what im confused at aswell

  • @roudoudou_3596

    @roudoudou_3596

    3 жыл бұрын

    Cuz that’s inside a square root, 1/x becomes 1/x^2

  • @brtjsst

    @brtjsst

    3 жыл бұрын

    everything that is placed from outside the square root to the inside got squared

  • @Mr-ep2qi
    @Mr-ep2qi2 жыл бұрын

    great video!

  • @reemhantoli6695
    @reemhantoli66954 жыл бұрын

    You are very very good

  • @shiema9920
    @shiema9920 Жыл бұрын

    I would like to ask 15:54 ? why is it like 1/x when the numerator is only 1? Thank you

  • @ChillExpressions

    @ChillExpressions

    Жыл бұрын

    same here, I'm confused at that part, did u figure it out?

  • @kalpanapatel7172
    @kalpanapatel71723 жыл бұрын

    Thank You so much Sir

  • @valkyrieeee203
    @valkyrieeee2033 ай бұрын

    I wanna ask 12:52, why denominator didn't multiply by 1/X^6? why only numerator ....

  • @colloidalsilver177
    @colloidalsilver1774 жыл бұрын

    @4:00 why are we multiplying the top and the bottom by 1/x”

  • @champagnestainedbirkin

    @champagnestainedbirkin

    4 жыл бұрын

    x was at the denominator. It was first 4/x then simply 4/1 multiplied by 1/x. In short he separated it. I hope this answer is helpful and sorry I replied 5 months later.

  • @jcpark1125

    @jcpark1125

    4 жыл бұрын

    @@champagnestainedbirkin what do you mean "first 4/x then simply 4/1 multiplied by 1/x. In short he separated it. " where did 4/x came from and 4/1?? anyways..whats the purpose of him multiplying (1/x) at the top and bottom?

  • @sophia_skip15letters

    @sophia_skip15letters

    4 жыл бұрын

    I think he does it to show WHY the limit of (8/3x+4) is equal to zero. Since he was already explaining why the limit of (1/x) is always zero, he made both the numerator and denominator in terms of (1/x) to prove his point. So you don't need to do it if you already get how and why the limit of the function is equal to zero, but he does it to explain it more thoroughly.

  • @user-kq6cs4tb4s
    @user-kq6cs4tb4s5 ай бұрын

    Why go to school when we have KZread

  • @tevinabeysekera6038
    @tevinabeysekera60382 жыл бұрын

    Thank you so much

  • @SuperEH2393
    @SuperEH23935 жыл бұрын

    wish i could write and listen as fast as you man

  • @vilarseirei
    @vilarseirei Жыл бұрын

    I have a test in an hour

  • @razaislamicchannel3518

    @razaislamicchannel3518

    2 ай бұрын

    😂😂😂

  • @user-se8mg3vy7n
    @user-se8mg3vy7n5 ай бұрын

    9:43 can someone tell me why he crossed out -8 and -5? He didn't go into detail

  • @mukandaedgar1168
    @mukandaedgar1168 Жыл бұрын

    When you multiplied 1/x with √9x^2 +, is it not suppose to be √9x+

  • @roneilboodie6735
    @roneilboodie67353 жыл бұрын

    IS IT THE SAMe if x aprroach infinity from the left (-)

  • @micah865
    @micah8653 жыл бұрын

    THANK YOUU VERY MUCH

  • @ayaelameer7779
    @ayaelameer77793 жыл бұрын

    11:53 why did we remove the x square pls?

  • @rabunitube
    @rabunitube Жыл бұрын

    Thanks my techer

  • @carterspringer48
    @carterspringer4810 ай бұрын

    Dude I fucking love you man thank you so much for making videos I know you get these kinds of comments on all your video but they help so much I just watched a 10 minute video from a University professor who basically explained nothing then to come here and learn everything in 2 minutes is crazy

  • @creature._.
    @creature._.10 ай бұрын

    My savior, year to year

  • @maryamkharal2444
    @maryamkharal24442 жыл бұрын

    Thank you for uploading this video! It was such a big help.