CPM Homework Help : APCALC Problem 7-207

Evaluate each of the following limits.

$\lim\limits _ { x \rightarrow 1 } \frac { \operatorname { ln } ( x ) } { x ^ { 2 } - 1 }$
Hint (a):
$\text{This is an indeterminate form: }\frac{0}{0}$
Use l'Hôpital's Rule.

$\lim\limits _ { x \rightarrow 0 ^ { + } } ( 1 + 5 x ) ^ { 2 / x }$
Hint (b):
Do you remember the definition of $e$ ?