### Home > CALC > Chapter 7 > Lesson 7.4.4 > Problem7-214

7-214.

Evaluate each limit.

1. $\lim\limits_ { x \rightarrow 0 } \frac { \operatorname { cos } 3 x - \operatorname { cos } x } { x ^ { 2 } }$

This is a indeterminate form: $\frac{0}{0}$
l'Hôpital's Rule may be applied.

1. $\lim\limits_ { x \rightarrow 0 } \frac { \operatorname { tan } x } { e ^ { x } - 1 }$

See the hint in part (a).

1. $\lim\limits_ { x \rightarrow 0 ^ { + } } ( \operatorname { cot } x - \operatorname { csc } x )$

1. $\lim\limits_ { x \rightarrow 0 } \frac { 2 ^ { x } } { x }$