Discuss the continuity of the function `f(x)={(sin2x)/x ,ifx<0x+2,ifxgeq0`

Explanation

f(x)= \begin{cases}\frac{\sin 2 x}{x}, & x<0 \\ x+2, & x \geqslant 0 \end{cases}


If any function is continuous at `x=a`

Left Hand Limit = Right hand Limit, `x=a`

$$
\begin{aligned}
&\text { LHL }=\lim _{x \rightarrow 0} \frac{\sin 2 x}{x}=\operatorname{Lim}_{x \rightarrow 0} 2 \cdot\left(\frac{\sin 2 x}{2 x}\right) \\
&\text { RHL } \quad \R H L=2 \\
...