Limit Involving Squeeze Theorem

The problem I have is

I know I have to use the squeeze theorem, by implementing the range of the cosine function; but when I do that I get

But that would imply the original limit would go to approach zero, but that is certainly not what the answer key attests. Am I setting up my range wrong?

Re: Limit Involving Squeeze Theorem

Do you have to use squeeze theorem? What about L'Opital's rule?

Re: Limit Involving Squeeze Theorem

Hello Bashyboy,

If we were to try to solve this problem with the squeeze theorem using the bound conditions for , we would have:

which doesn't really help us at all.

Provided you are allowed to use L'Hospital's Rule, we can say:

and...

so...

If you HAVE to use the squeeze theorem, just play around with functions that are ALWAYS outside of the bounds of and see what happens. Good luck!

Re: Limit Involving Squeeze Theorem

Ah, yes, that would be profoundly simple. Though, I wonder, would it be possible to do the squeeze theorem?

Re: Limit Involving Squeeze Theorem

I'm not really sure if you can do the squeeze theorem here. If it is possible, I definitely can't think of the bound functions at the moment lol.

Re: Limit Involving Squeeze Theorem

not a squeeze, but not L'Hopital either ...

now take the limit as ...

Re: Limit Involving Squeeze Theorem

How do you find limit of sinx/x without L'hospital? That's not easier than original

Quote:

Originally Posted by

**skeeter**

Re: Limit Involving Squeeze Theorem

Quote:

Originally Posted by

**httr** How do you find limit of sinx/x without L'hospital? That's not easier than original

at the start of most calculus courses, one learns the geometric proof of

this basic trig limit is required in finding the derivative of using first principles ...