Problem that I don't know how to setup

• Sep 10th 2008, 07:57 PM
66replica
Problem that I don't know how to setup
Use the sandwich theorem to explain why
$\displaystyle \lim_{x \rightarrow \ 0}x^2*cos(1/x)=0$

Should I pick two other functions around this function and solve for their limits? What would be two good functions to pick?
• Sep 10th 2008, 08:02 PM
jenius
Quote:

Originally Posted by 66replica
Use the sandwich theorem to explain why
$\displaystyle \lim_{x \rightarrow \ 0}x^2*cos(1/x)=0$

Should I pick two other functions around this function and solve for their limits? What would be two good functions to pick?

Yes, pick two other functions. You want a function that is always greater than or equal to, and one that is always less than or equal to your function. Since cos(x) is always less than or equal to 1, the function x^2 is always greater than your function. I'll let you figure out the lower function.
• Sep 11th 2008, 05:05 AM
Showcase_22
I have yet to study this at university but I did this:

http://i116.photobucket.com/albums/o...sproblem28.jpg

And a graph of it shows:

http://i116.photobucket.com/albums/o...SPROBLEM27.jpg

So it seems to work well.