Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \sin ( 5 x ) } { x }$ ?

A) $- \frac { 1 } { 5 }$
B) $\frac { 1 } { 5 }$
C)-5
D)5
E)Does not exist

Question

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \sin ( 5 x ) } { x }$ ?

A) $- \frac { 1 } { 5 }$
B) $\frac { 1 } { 5 }$
C)-5
D)5
E)Does not exist

Quizplus · Accepted Answer

The limit $\lim _ { x \rightarrow 0 } \frac { \sin ( 5 x ) } { x }$ can be solved by using the standard limit $\lim _ { x \rightarrow 0 } \frac { \sin ( x ) } { x } = 1$. By substituting $5x$ for $x$, the limit becomes $\lim _ { x \rightarrow 0 } \frac { \sin ( 5 x ) } { 5x } \cdot 5 = 1 \cdot 5 = 5$, hence the answer is 5.

Which of the Following Is Equal to Limit lim⁡x→0sin⁡(5x)x\lim _ { x \rightarrow 0 } \frac { \sin ( 5 x ) } { x }limx→0​xsin(5x)​

Which of the Following Is Equal to Limit $\lim _ { x \rightarrow 0 } \frac { \sin ( 5 x ) } { x }$