Use l'Hopital's Rule to evaluate the limit.
-$\lim _ { x - 0} \frac { \sin 5 x } { \sin x }$
A) 0
B) -5
C) 1
D) 5

Name: Use l'Hopital's Rule to evaluate the limit. -$\lim _ { x - 0} \frac { \sin 5 x } { \sin x }$ A) 0 B) -5 C) 1 D) 5
Brand: Quizplus
Rating: 4.9 (32 reviews)

Question

Quizplus · Accepted Answer

When we try to substitute x = 0, we get an indeterminate form 0/0, which means we can use L'Hopital's Rule.
\begin{align*}
\lim_{x	o0}\frac{\sin5x}{\sin x} &= \lim_{x	o0}\frac{5\cos5x}{\cos x} \
&= \frac{5\cos0}{\cos0} \
&= 5
\end{align*}
Therefore, the answer is D.

Use L'Hopital's Rule to Evaluate the Limit lim⁡x−0sin⁡5xsin⁡x\lim _ { x - 0} \frac { \sin 5 x } { \sin x }limx−0​sinxsin5x​

Use L'Hopital's Rule to Evaluate the Limit $\lim _ { x - 0} \frac { \sin 5 x } { \sin x }$