Provide an appropriate response.
-It can be shown that the inequalities $1 - \frac { x ^ { 2 } } { 6 }

Question

Provide an appropriate response.
-It can be shown that the inequalities $1 - \frac { x ^ { 2 } } { 6 } < \frac { x \sin ( x ) } { 2 - 2 \cos ( x ) } < 1$ hold for all values of $x$ close to zero. What, if anything, does this tell you about $\frac { x \sin ( x ) } { 2 - 2 \cos ( x ) }$ ? Explain.

Quizplus · Accepted Answer

The Answer of Provide an appropriate response.
-It can be shown that the inequalities $1 - \frac { x ^ { 2 } } { 6 } < \frac { x \sin ( x ) } { 2 - 2 \cos ( x ) } < 1$ hold for all values of $x$ close to zero. What, if anything, does this tell you about $\frac { x \sin ( x ) } { 2 - 2 \cos ( x ) }$ ? Explain.

Provide an Appropriate Response 1−x26<xsin⁡(x)2−2cos⁡(x)<11 - \frac { x ^ { 2 } } { 6 } < \frac { x \sin ( x ) } { 2 - 2 \cos ( x ) } < 11−6x2​<2−2cos(x)xsin(x)​<1

Provide an Appropriate Response $1 - \frac { x ^ { 2 } } { 6 } < \frac { x \sin ( x ) } { 2 - 2 \cos ( x ) } < 1$