Prove the following

Question:

If $f(x)= \begin{cases}\frac{\sin (a+2) x+\sin x}{x} ; & x<0 \\ b & ; x=0 \\ \frac{\left(x+3 x^{2}\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{x^{\frac{4}{3}}} & ; x>0\end{cases}$

is continuous at $x=0$, then $a+2 b$ is equal to :

  1. $-1$

  2. 1

  3. $-2$

  4. 0


Correct Option: , 4

Solution:

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