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

Question

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

Quizplus · Accepted Answer

As $x$ approaches 0, the value of $\sin x$ approaches 0 as well, and since $f(x) = x \sin x$, the product of $x$ and $\sin x$ also approaches 0. Therefore, $f(x)$ approaches 0 as $x$ approaches 0.

Describe the Behavior of the Function Below as X Approaches f(x)=xsin⁡xf ( x ) = x \sin xf(x)=xsinx

Describe the Behavior of the Function Below as X Approaches $f ( x ) = x \sin x$