# Evaluate the limit using the squeeze theorem?

• October 17th 2009, 12:02 PM
REWIND10
Evaluate the limit using the squeeze theorem?

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

any help is appreciated!
• October 17th 2009, 01:03 PM
Since $-1 \leq \cos(\pi/x) \leq 1$ we have...
$x e^{-1} \leq x e^{\cos(\pi/x)} \leq x e^1$.
$0 \leq x e^{\cos(\pi/x)} \leq 0$.
So by the squeeze theorem. $\lim_{x \rightarrow 0} e^{\cos(\pi/x)} = 0$.