Provide an appropriate response.
-The inequality $1 - \frac { x ^ { 2 } } { 2 }

Question

Provide an appropriate response.
-The inequality $1 - \frac { x ^ { 2 } } { 2 } < \frac { \sin x } { x } < 1$ holds when $x$ is measured in radians and $| x | < 1$. Find $\lim _ { x \rightarrow \theta } \frac { \sin x } { x }$ if it exists.
A) 0
B) does not exist
C) 1
D) $0.0007$

Quizplus · Accepted Answer

The inequality shows that as x approaches 0, sin(x) approaches x (since sin(x) is approximately x when x is small). Therefore, the limit as x approaches 0 of sin(x)/x is 1.

Provide an Appropriate Response 1−x22<sin⁡xx<11 - \frac { x ^ { 2 } } { 2 } < \frac { \sin x } { x } < 11−2x2​<xsinx​<1

Provide an Appropriate Response $1 - \frac { x ^ { 2 } } { 2 } < \frac { \sin x } { x } < 1$