Exercise 23

Determine the appropriate symbol to write after an equal sign following each of the given limits. In each case, the appropriate symbol is either a real number, $\infty$, or $-\infty$. Also, state whether or not each limit exists and if the limit exists prove its existence (and value) by applying the appropriate limit laws. The Rational Limit Forms table in Limit Laws summarizes strategies to be employed based upon the initial form of the limit.

$\lim\limits_{x\to0^{+}}\dfrac{\fe{\ln}{x^e}}{\fe{\ln}{e^x}}$