Evaluate the limit using the squeeze theorem?

**REWIND10** · October 17th 2009, 11:02 AM

lim (x-->0) xe^cos(pi/x)

any help is appreciated!

**Deadstar** · October 17th 2009, 12:03 PM

I'm not 100% sure if this is right but this is certainly what I would do...
Since $-1 \leq \cos(\pi/x) \leq 1$ we have...

$x e^{-1} \leq x e^{\cos(\pi/x)} \leq x e^1$ .

So taking limits as x->0 we get...

$0 \leq x e^{\cos(\pi/x)} \leq 0$ .

So by the squeeze theorem. $\lim_{x \rightarrow 0} e^{\cos(\pi/x)} = 0$ .

Think that's right but hopefully someone will drop by to confirm.
I also checked the limit with MAPLE and it came out to be 0 as well.

Thread: Evaluate the limit using the squeeze theorem?

LinkBack

Thread Tools

Display

Evaluate the limit using the squeeze theorem?

Similar Math Help Forum Discussions

Need help with example of Squeeze Theorem

Squeeze Theorem

squeeze theorem

Using the Squeeze Theorem to find a limit.

Squeeze Theorem

Search Tags