1. ## limit help please!!

how do i prove lim (x^2) * (cos(1/x)) = 0
as x approaches 0
please can you list the steps

2. ## Re: limit help please!!

Note that cos(1/x) is bounded, no matter how rapidly it oscilates when x is near 0. Then apply the squeeze theorem.

3. ## Re: limit help please!!

Originally Posted by johnsomeone
Note that cos(1/x) is bounded, no matter how rapidly it oscilates when x is near 0. Then apply the squeeze theorem.
Or just the fact that the product of a function that goes to 0 with a bounded function is 0.

4. ## Re: limit help please!!

ok then how do i prove it on a 10 point free response question. can someone please list out the steps so that i can understand for future tests because i only got 3/10 for this question on the test

5. ## Re: limit help please!!

Originally Posted by ubhutto
ok then how do i prove it on a 10 point free response question. can someone please list out the steps so that i can understand for future tests because i only got 3/10 for this question on the test
$-1\le\cos\left(\tfrac{1}{x}\right)\le 1$ thus $-x^2\le x^2\cos\left(\tfrac{1}{x}\right)\le x^2$

Both $\lim _{x \to 0} - x^2 = 0 = \lim _{x \to 0} x^2$.