10 Limits at Infinity

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10 Calculus Limits

Do you have what it takes to calculate 10 limits at infinity? In this video I show you standard technicians for dealing with those limits

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20:06 Wait a minute... Functions can go to hell ?!

bahadirtuncay

First time I ever saw a good explanation of the Squeeze Theorem. Thank you!

Mosux

the best video I've seen on this concept, thank you

intuitiveclass

Esse canal tem um ótimo conteúdo. Parabéns pelo trabalho!

thomasroberto

I think I learn (or possibly re-learn) something new in every video.

garyhuntress

brilliant exercises thank you so much ❤

kirathefirst

For 9, it's a bit tempting to first evaluate the e^(-x) terms to 0 then cancel e^(x)/e^(x) to 1. That is not rigorous, but gives the right answer in this case. Going forward, could you show an example where getting rid of a term that appears to go zero early on like that actually gives the wrong answer?

Gameboygenius

Another way of saying two wrongs might make a write is: "my exes cancel out nicely"

Gamma_Digamma

Thank you Im now more confident for the AP exam

HeyKevinYT

For limit 6, as x goes to infinity(and so does what is inside the square root), you could just add a +1 inside the square root, getting sqrt(x^2+2x+1), which is just abs(x+1), that, because x goes to -inf, becomes -x-1, so the original limit is reduced to x+(-x-1), so -1, which is the same result as you got.

Btw it can be proven that the difference between sqrt(ax^2+bx+c) and sqrt (ax^2+bx), where a, b and c are constants, goes to zero as x goes to infinity.

dantop

Hang on! In example 6 are you saying sqrt(x^2) for negative x is negative? You could take either the positive or the negative sqrt but why preference the negative? The resulting limit is the same anyway so it doesn't matter in this case.

davannaleah

Please explain hypergeometric series and finding them when they're solutions to integrations, as in ∫tanⁿ(ax)dx, which, according the integral table involves a hypergeometric series.

ChefSalad