Given sin x/ x^2 how do you find the limit as x approaches 0?

Jul 9, 2016

You should use the fact that $\lim \sin \frac{x}{x} = 1$ as $x$ approaches 0

Explanation:

You can modify the expression as follows:

$\sin \frac{x}{x} ^ 2 = \sin \frac{x}{x} \cdot \frac{1}{x}$, and then taking the limits:

$\lim \sin \frac{x}{x} = 1$, and

$\lim \frac{1}{x} = \infty$, so the end result is:

$\lim \sin \frac{x}{x} ^ 2 = \lim \sin \frac{x}{x} \cdot \lim \frac{1}{x} = 1 \cdot \infty = \infty$