Limits at Infinity & Horizontal Asymptotes

[@TheOrganicChemistryTutor]

Limits - Free Formula Sheet: bit.ly/3T3dD2X Limits - Video Lessons: www.video-tutor.net/limits.html

[@inemibok]

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 ❤️

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

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

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

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[@samiulislamdurjoy]

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

[@youssefosama4466]

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[@TheOrganicChemistryTutor]

Thanks

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[@tranquoclan5043]

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).

[@nicholasachuz8329]

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.

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[@hooligan1602]

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!

[@maryam4587]

"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]

thank youuuu I was confused on that

[@kofi4927]

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

[@ThornedRose134]

You made limits so so so so so so so so soooooo much easier. Thank you. For realsies.

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

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[@kurokubushi]

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.

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[@carolnoelle2468]

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

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[@hazimrassam9389]

At 11:35 the answer should be -2 because when x enters inside the square root it becomes x^2 and you have to multiply the limit by a negative sign.

[@pablogonzalez3705]

What you are saying is true when x -> - infinity, not when x -> infinity

[@5nanometers]

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]

"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!

[@MohitBaboria]

Because √(x²) = x for x ≥ 0

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This was so unbelievably helpful thank you

[@strugglingcollegestudent]

this is so much easier I honestly wish they taught us in precalc

[@neutronzz3543]

So ur learning calculus in precalculus makes no sense

[@michellecampa9850]

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]

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

[@geraldengmann5643]

​@@plon5284 I still don't get

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I don t have any test . But it looks more fun than boring algebra i study in school. That s why i am learning this for fun

[@jonnydobandliamried8094]

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

[@glance7335]

12:28 HOW DO YOU DECIDE WHICH FRACTION YOU SHOULD MULTIPLY WITH

[@dagatejohnelo.6153]

Thank your so much ,I really struggling to this

[@delulus_0]

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]

same question

[@korcakd2]

Because he got rid of it in the numerator and in the denominator it’s inside a square root. Therefore, x is the highest

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wish i could write and listen as fast as you man

[@shiema9920]

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

[@ChillExpressions]

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

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[@jayantijally5258]

Sir please solve the question. Evaluate lim n tends to infinite x to the power n divided by e to the power x

[@VndNvwYvvSvv]

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.

[@sarafeliciano3088]

Amazing video! Cheers!!

[@elis2506]

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?

[@nickareekadan7313]

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??

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Same question right here too😂😅

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[@jeanetteann8189]

15:50 dude, when did 9x^2 divided by x became 9??

[@Jacobk2403]

since it is inside a root, you have to divide by 1/x^2 and not 1/x

[@uba_Michael10]

@@Jacobk2403 thanks boss I understand ur point clearly

[@hanslarrobis117]

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

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Life saver 🤝🏾💯

[@realrishiiscoolgaming9548]

my sir took x^m as common and divide so we have up to x^3 so we can write it as a(1/X^1or 2 or 3)=a(0)=0

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