Mathematics

Mathematics

Problem

The function gg is defined by g(x)={xsin⁡(2x)1−cos⁡(3x),x<0,tan⁡(5x)x,x≥0.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 lim⁡x→0g(x)\displaystyle\lim_{x\to 0} g(x) exists. If it exists, state its value.

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