Question

limxtends to 0 x^3cotx​

Answer 1

$\displaystyle\lim_{x\to0}\ x^3\cot x\ =\ \lim_{x\to0}\ \dfrac{x^3}{\tan x}$

On giving the value 0 directly to x, we get the limit in indeterminate form. So we apply L'hospital's rule.

So,

$\displaystyle\lim_{x\to0}\ \dfrac{x^3}{\tan x}\ =\ \lim_{x\to0}\ \dfrac{3x^2}{\sec^2 x}\ =\ \dfrac{3\cdot0^2}{1^2}\ =\ \mathbf{0}$

Hence, 0 is the answer.