Question

limxtends to 0 ((tanx-sinx)/x^3

Answer 1

please find attached solution

Answer 2

Given:

$\lim_{x\rightarrow 0}\frac{tanx-sinx}{x^3}$

To find:

Value of $\lim_{x\rightarrow 0}\frac{tanx-sinx}{x^3}$

Solution:

$\lim_{x\rightarrow 0}\frac{tanx-sinx}{x^3}$ (0/0 form)

Now, applying L'hospital rule

$\lim_{x\rightarrow 0}\frac{sec^2x-cosx}{3x^2}$(0/0 form)

Again,applying L'hospital rule

$\lim_{x\rightarrow 0}\frac{2sec^2xtanx+sinx}{6x}$(0/0 form)

Again,applying L'hospital rule

$\lim_{x\rightarrow 0}\frac{4sec^2xtanx+2sec^4x+cosx}{6}$

=$\frac{3}{6}=\frac{1}{2}$