Find the indicated limit.
-$$\lim _ { x \rightarrow \infty } \left( e ^ { - x ^ { 2 } } \sin x \right)$$
A) $- \infty$
B) 0
C) $\infty$
D) $- 1$

Question

Quizplus · Accepted Answer

The exponential function $e^{-x^2}$ approaches 0 as $x$ approaches infinity much faster than any polynomial or trigonometric function can grow. Therefore, the product $e^{-x^2} \sin x$ will also approach 0 as $x$ approaches infinity, regardless of the oscillating nature of $\sin x$.

Find the Indicated Limit lim⁡x→∞(e−x2sin⁡x)\lim _ { x \rightarrow \infty } \left( e ^ { - x ^ { 2 } } \sin x \right)x→∞lim​(e−x2sinx)

Find the Indicated Limit $\lim _ { x \rightarrow \infty } \left( e ^ { - x ^ { 2 } } \sin x \right)$