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10-114.

Evaluate the following limits.

$\lim\limits_ { x \rightarrow 4 } \frac { \sqrt { x } - 2 } { x - 4 }$
Hint (a):
The denominator can be factored as:
$(\sqrt{x}+2)(\sqrt{x}-2)$

$\lim\limits_ { x \rightarrow 0 } \frac { 2 ^ { x } - 3 ^ { x } } { x ^ { 2 } }$
Hint (b):
Use l'Hôpital's Rule, but only once.

$\lim\limits_ { x \rightarrow 1 ^ { + } } \frac { \operatorname { ln } x } { \sqrt { x - 1 } }$
Hint (c):
Use l'Hôpital's Rule twice.

$\lim\limits_ { x \rightarrow 0 ^ { + } } \frac { \operatorname { ln } x } { e ^ { 1 / x } }$
Step (d):
$=\lim\limits_{x\to 0^+}\frac{1/x}{e^{1/x}(-x^{-2})}$

$\lim\limits_ { x \rightarrow \pi / 2 } \frac { \operatorname { sec } x } { \operatorname { sec } ( 2 x ) }$
Hint (e):
Rewrite the argument of the limit as: ?

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