Find the limit
$\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x }$
A) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 5$
B) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 4$
C) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = - 3$
D) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = - 5$
E) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 3$

Question

Find the limit 
 $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x }$ 
A) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 5$
B) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 4$
C) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = - 3$
D) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = - 5$
E) $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 3$

Quizplus · Accepted Answer

The limit can be solved by using the standard limit $\lim _ { x \rightarrow 0 } \frac { \sin x } { x } = 1$. By substituting $3x$ for $x$, the limit becomes $\lim _ { x \rightarrow 0 } \frac { \sin 3x } { 3x } \cdot 3 = 3\cdot 1 = 3$.

Find the Limit lim⁡x→0sin⁡3xx\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x }limx→0​xsin3x​

Find the Limit $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x }$