Find the indicated limit.
-$$\lim _ { x \rightarrow \infty } \frac { \cos \left( \frac { 2 } { x } \right) } { 5 + \frac { 2 } { x } }$$
A) $\frac { 1 } { 5 }$
B) 0
C) Does not exist
D) $- \frac { 1 } { 5 }$

Question

Quizplus · Accepted Answer

As $x$ approaches infinity, $\frac{2}{x}$ approaches 0. Therefore, $\cos\left(\frac{2}{x}\right)$ approaches $\cos(0) = 1$, and the denominator approaches $5 + 0 = 5$. Thus, the limit is $\frac{1}{5}$.

Find the Indicated Limit lim⁡x→∞cos⁡(2x)5+2x\lim _ { x \rightarrow \infty } \frac { \cos \left( \frac { 2 } { x } \right) } { 5 + \frac { 2 } { x } }x→∞lim​5+x2​cos(x2​)​

Find the Indicated Limit $\lim _ { x \rightarrow \infty } \frac { \cos \left( \frac { 2 } { x } \right) } { 5 + \frac { 2 } { x } }$