Find the limit
$\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x }$
A) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = 6$
B) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = - 7$
C) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = - 5$
D) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = 5$
E) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = 7$

Question

Find the limit 
 $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x }$
A) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = 6$
B) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = - 7$
C) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = - 5$
D) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = 5$
E) $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x } = 7$

Quizplus · Accepted Answer

The limit can be solved using the standard limit $\lim _ { x \rightarrow 0 } \frac { \tan x } { x } = 1$. By substituting $x$ with $5x$, the limit becomes $\lim _ { x \rightarrow 0 } \frac { \tan 5x } { 5x } \cdot 5 = 5$, because multiplying and dividing by 5 adjusts for the change in variable, resulting in the answer being 5.

Find the Limit lim⁡x→0tan⁡5xx\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x }limx→0​xtan5x​

Find the Limit $\lim _ { x \rightarrow 0 } \frac { \tan 5 x } { x }$