Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \cos ^ { 2 } ( 3 x ) - 1 } { 5 x }$ ?

A) $- \frac { 6 } { 5 }$
B) $- \frac { 5 } { 6 }$
C)0
D) $\frac { 5 } { 6 }$
E) $\frac { 6 } { 5 }$

Question

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \cos ^ { 2 } ( 3 x ) - 1 } { 5 x }$ ?

A) $- \frac { 6 } { 5 }$
B) $- \frac { 5 } { 6 }$
C)0
D) $\frac { 5 } { 6 }$
E) $\frac { 6 } { 5 }$

Quizplus · Accepted Answer

Using the limit laws, we have:$$\lim_{x	o 0} \frac{\cos^2(3x) - 1}{5x} = \lim_{x	o 0} \frac{\cos^2(3x) - 1}{3x} \cdot \frac{3x}{5x} = \lim_{x	o 0} \frac{\cos^2(3x) - 1}{3x} \cdot \lim_{x	o 0} \frac{3x}{5x}$$$$= \lim_{x	o 0} \frac{\cos^2(3x) - 1}{3x} \cdot \frac{3}{5} = \lim_{x	o 0} \frac{\cos^2(3x) - 1}{3x} \cdot \frac{1}{5}$$$$= \lim_{x	o 0} \frac{\cos^2(3x) - 1}{3x} \cdot \lim_{x	o 0} \frac{1}{5} = 0 \cdot \frac{1}{5} = 0$$

Which of the Following Is Equal to Limit lim⁡x→0cos⁡2(3x)−15x\lim _ { x \rightarrow 0 } \frac { \cos ^ { 2 } ( 3 x ) - 1 } { 5 x }limx→0​5xcos2(3x)−1​

Which of the Following Is Equal to Limit $\lim _ { x \rightarrow 0 } \frac { \cos ^ { 2 } ( 3 x ) - 1 } { 5 x }$