Describe the behavior of the function below as x approaches zero. $$f ( x ) = \frac { | x | } { 3 } \sin x$$
A)f → -∞ as x → 0.
B)f → -1 as x → 0.
C)f → 1 as x → 0.
D)f → +∞ as x → 0.
E)f → 0 as x → 0.

Question

Describe the behavior of the function below as x approaches zero.​ $$f ( x ) = \frac { | x | } { 3 } \sin x$$ ​
A)f → -∞ as x → 0.
B)f → -1 as x → 0.
C)f → 1 as x → 0.
D)f → +∞ as x → 0.
E)f → 0 as x → 0.

Quizplus · Accepted Answer

As $x$ approaches zero, the absolute value of $x$, $|x|$, also approaches zero. Since $\sin(x)$ is bounded between -1 and 1, the product of $|x|/3$ and $\sin(x)$ will also approach zero. Therefore, $f(x)$ approaches 0 as $x$ approaches 0.

Describe the Behavior of the Function Below as X Approaches f(x)=∣x∣3sin⁡xf ( x ) = \frac { | x | } { 3 } \sin xf(x)=3∣x∣​sinx

Describe the Behavior of the Function Below as X Approaches $f ( x ) = \frac { | x | } { 3 } \sin x$