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

any help is appreciated!

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- Oct 17th 2009, 11:02 AMREWIND10Evaluate the limit using the squeeze theorem?

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

any help is appreciated! - Oct 17th 2009, 12:03 PMDeadstar
I'm not 100% sure if this is right but this is certainly what I would do...

Since $\displaystyle -1 \leq \cos(\pi/x) \leq 1$ we have...

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

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

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

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

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.