CPM Homework Help : APCALC Problem 7-220

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Home > APCALC > Chapter 7 > Lesson 7.4.4 > Problem 7-220

7-220.

Evaluate each limit.

$\lim\limits _ { x \rightarrow 0 } \frac { \operatorname { cos } ( 3 x ) - \operatorname { cos } ( x ) } { x ^ { 2 } }$
Hint (a):
$\text{This is an indeterminate form: }\frac{0}{0}$
l'Hôpital's Rule may be applied.

$\lim\limits _ { x \rightarrow 0 } \frac { \operatorname { tan } ( x ) } { e ^ { x } - 1 }$
Hint (b):
See the hint in part (a).

$\lim\limits _ { x \rightarrow 0 ^ { + } } ( \operatorname { cot } ( x ) - \operatorname { csc } ( x ) )$
Hint (c):
$\cot(x)-\csc(x)=\frac{\cos(x)-1}{\sin(x)}$

$\lim\limits _ { x \rightarrow 0 } \frac { 2 ^ { x } } { x }$
Hint (d):
$y=\frac{2^{x}}{x}\text{ has a vertical asymptote at }x=0,$ $\text{ so the limit}\rightarrow +\infty \text{ or }-\infty. \text{ Which one?}$

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