Question

Find the
$\underset{x\to 0}{lim}\frac{3\sin x-{\sin }^{3}x}{x^3}$

Answer 1

$\underset{x\to 0}{lim}\frac{3\sin x-{\sin }^{3}x}{x^3}$

$\underset{x\to 0}{lim}3\left(\frac{\sin x}{x}\right)\times \frac{1}{x^2}-{\left(\frac{\sin x}{x}\right)}^3$

we know that $\underset{x\to 0}{lim}\frac{\sin x}{x}=1$

$\underset{x\to 0}{lim}\frac{3}{x^2}-1$

$\frac{3}{x^2}$ is $\frac{3}{0}$ which is not defined.

So limit does not exist