Determine the limit algebraically, if possible.
-$$\lim _ { x \rightarrow0 } \frac { 6 x } { 2 \sin x }$$
A) 0
B) Does not exist
C) 3
D) 1

Question

Quizplus · Accepted Answer

The limit can be simplified using the identity $\lim _ { x \rightarrow 0 } \frac { \sin x } { x } = 1$. By rearranging the given expression, we get $\lim _ { x \rightarrow 0 } \frac { 6 x } { 2 \sin x } = \lim _ { x \rightarrow 0 } \frac { 6 } { 2 } \cdot \frac { x } { \sin x }$. Since $\lim _ { x \rightarrow 0 } \frac { x } { \sin x } = 1$, the expression simplifies to $3 \cdot 1 = 3$.

Determine the Limit Algebraically, If Possible lim⁡x→06x2sin⁡x\lim _ { x \rightarrow0 } \frac { 6 x } { 2 \sin x }x→0lim​2sinx6x​

Determine the Limit Algebraically, If Possible $\lim _ { x \rightarrow0 } \frac { 6 x } { 2 \sin x }$