Find the value of the limit $\lim _ { x \rightarrow 0 } \frac { \tan 2 x } { x }$ .
A)4
B)1
C) $\frac { 1 } { 4 }$
D)2
E) $\frac { 1 } { 2 }$
F)0
G) $\frac { 1 } { 3 }$
H)3

Question

Find the value of the limit $\lim _ { x \rightarrow 0 } \frac { \tan 2 x } { x }$ .
A)4
B)1
C) $\frac { 1 } { 4 }$
D)2
E) $\frac { 1 } { 2 }$ 
F)0
G) $\frac { 1 } { 3 }$ 
H)3

Quizplus · Accepted Answer

The limit can be solved by recognizing it as a standard limit form. We use the fact that $\lim _ { x \rightarrow 0 } \frac { \sin x } { x } = 1$. By rewriting $\tan 2x$ as $\frac{\sin 2x}{\cos 2x}$ and noting that $\cos 2x$ approaches 1 as $x$ approaches 0, we can focus on the $\sin 2x$ part. The limit becomes $\lim _ { x \rightarrow 0 } \frac { 2\sin 2x } { 2x }$ because we can multiply and divide by 2 to match the standard limit form. This simplifies to $2 \cdot \lim _ { x \rightarrow 0 } \frac { \sin 2x } { 2x } = 2 \cdot 1 = 2$, using the standard limit for sine.

Find the Value of the Limit lim⁡x→0tan⁡2xx\lim _ { x \rightarrow 0 } \frac { \tan 2 x } { x }limx→0​xtan2x​

Find the Value of the Limit $\lim _ { x \rightarrow 0 } \frac { \tan 2 x } { x }$