Describe the behavior of the function below as x approaches zero.
$f ( x ) = \frac { | x | } { 5 } \cos ( x )$
A)f $\rightarrow$ +$\infty$ as x $\rightarrow$ 0.
B)f $\rightarrow$ 1 as x $\rightarrow$ 0.
C)f $\rightarrow$ 0 as x $\rightarrow$ 0.
D)f $\rightarrow$ –1 as x $\rightarrow$ 0.
E)f $\rightarrow$ –$\infty$ as x $\rightarrow$ 0.

Question

Describe the behavior of the function below as x approaches zero. 
 $f ( x ) = \frac { | x | } { 5 } \cos ( x )$ 
A)f $\rightarrow$ +$\infty$ as x $\rightarrow$ 0. 
B)f $\rightarrow$ 1 as x $\rightarrow$ 0. 
C)f $\rightarrow$ 0  as x $\rightarrow$ 0. 
D)f $\rightarrow$ –1 as x $\rightarrow$ 0. 
E)f $\rightarrow$ –$\infty$ as x $\rightarrow$ 0.

Quizplus · Accepted Answer

The function $f(x) = \frac{|x|}{5}\cos(x)$ approaches 0 as $x$ approaches 0 because the numerator $|x|$ approaches 0, and $\cos(x)$ approaches 1. The product of something approaching 0 and something finite (1 in this case) is 0.

Describe the Behavior of the Function Below as X Approaches f(x)=∣x∣5cos⁡(x)f ( x ) = \frac { | x | } { 5 } \cos ( x )f(x)=5∣x∣​cos(x)

Describe the Behavior of the Function Below as X Approaches $f ( x ) = \frac { | x | } { 5 } \cos ( x )$