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

Question

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

Quizplus · Accepted Answer

As $x$ approaches 0, $|x|$ approaches 0, and $\cos(x)$ approaches $\cos(0) = 1$. The product of a number approaching 0 and a number approaching 1 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 $f ( x ) = \frac { | x | } { 5 } \cos ( x )$