Determine the limit algebraically, if possible.
-$$\lim _ { x \rightarrow0 } \frac { 10 \sin x } { 6 x }$$
A) Does not exist
B) 0
C) 1
D) $\frac { 5 } { 3 }$

Question

Determine the limit algebraically, if possible.
-$$\lim _ { x \rightarrow0   } \frac { 10 \sin x } { 6 x }$$
A) Does not exist
B) 0
C) 1
D) $\frac { 5 } { 3 }$

Quizplus · Accepted Answer

The limit can be simplified using the trigonometric limit $\lim _ { x \rightarrow 0 } \frac { \sin x } { x } = 1$. Thus, $\lim _ { x \rightarrow 0 } \frac { 10 \sin x } { 6 x } = \frac { 10 } { 6 } \times \lim _ { x \rightarrow 0 } \frac { \sin x } { x } = \frac { 10 } { 6 } \times 1 = \frac { 5 } { 3 }$.

Determine the Limit Algebraically, If Possible lim⁡x→010sin⁡x6x\lim _ { x \rightarrow0 } \frac { 10 \sin x } { 6 x }x→0lim​6x10sinx​

Determine the Limit Algebraically, If Possible $\lim _ { x \rightarrow0 } \frac { 10 \sin x } { 6 x }$