Consider the graph of the function and approximate $\lim _ { x \rightarrow 0 } \frac { \sin ( 8 x ) } { x }$, if it exists.

A) 1
B) 4
C) 8
D) $- 1$
E) The limit does not exist.

Question

Consider the graph of the function and approximate $\lim _ { x \rightarrow 0 } \frac { \sin ( 8 x ) } { x }$, if it exists.

A) 1 
B) 4 
C) 8 
D) $- 1$ 
E) The limit does not exist.

Quizplus · Accepted Answer

The limit can be evaluated by direct substitution:
$$\lim_{x\rightarrow0}\frac{\sin(8x)}{x}=\frac{\sin(8\cdot0)}{0}=8.$$
Therefore, the answer is (C) 8.

Consider the Graph of the Function and Approximate lim⁡x→0sin⁡(8x)x\lim _ { x \rightarrow 0 } \frac { \sin ( 8 x ) } { x }limx→0​xsin(8x)​

Consider the Graph of the Function and Approximate $\lim _ { x \rightarrow 0 } \frac { \sin ( 8 x ) } { x }$