Question

lim x-->0 [(xe^(1/x))/(lnx^sinx)]

anyone plz can help me on this question..

Answer 1

\[\lim_{x \rightarrow 0}\frac{e^{\frac{1}{x}}}{\ln(x)^{\sin(x)}}\]??

Answer 2

\[\lim_{x \rightarrow 0}\frac{xe^{\frac{1}{x}}}{\ln(x)^{\sin(x)}}\]

Answer 3

tried using l'hopital's rule and it just go way uglier. the wolf says one way it is zero and the other way is infinity
http://www.wolframalpha.com/input/?i=limit+as+x+goes+to+0+%28xe%5E%281%2Fx%29%29%2F%28ln%28x%29%5Esin%28x%29%29