lim (x-->0) xe^cos(pi/x)
any help is appreciated!
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.