Describe the behavior of the function below as x approaches zero. $$f ( x ) = | 5 x \cos x |$$
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.​ $$f ( x ) = | 5 x \cos x |$$ ​
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, $\cos x$ approaches $\cos(0) = 1$, and $5x$ approaches 0. Therefore, $|5x \cos x|$ approaches $|0 \cdot 1| = 0$.

Describe the Behavior of the Function Below as X Approaches f(x)=∣5xcos⁡x∣f ( x ) = | 5 x \cos x |f(x)=∣5xcosx∣

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