If f(x)=cases(a+2)x+ xx, & x0cases is continuous at …

Question

If $f(x)=\begin{cases}\dfrac{\sin(a+2)x+\sin x}{x}, & x<0\b, & x=0\\dfrac{(x+3x^2)^{1/3}-x^{1/3}}{x^{4/3}}, & x>0\end{cases}$ is continuous at $x=0$, then $a+2b$ is equal to:

Accepted Answer

LHL $=(a+2)+1=a+3$.

RHL $=\displaystyle\lim_{h	o0}\frac{(1+3h)^{1/3}-1}{h}=1$.

Continuity: $a+3=b=1\Rightarrow a=-2,\ b=1$. So $a+2b=-2+2=0$.

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