The function is defined by g(x)= cases x (2x) 1- (3x) , & x<0, [6pt] (5x) x , & x 0

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

The function

g

is defined by

g(x)=\begin{cases}\dfrac{x\sin(2x)}{1-\cos(3x)}, & x<0, \\[6pt] \dfrac{\tan(5x)}{x}, & x\ge 0.\end{cases}

Determine whether

\displaystyle\lim_{x\to 0} g(x)

exists. If it exists, state its value.