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

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Correct option is B

We have left hand limit as a+3,f(0)=b and right-hand limit is limh→0(1+3h)13-1h=1For it to be continuous, left hand limit is equal to the right-hand limit and it is also equal to f0 So, we get a=-2,b=1 and a+2b=0

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If fx=sin(a+2)x+sinxx;x<0b;x=0x+3x21/3-x1/3x4/3;x>0 is continuous at x=0 , then a+2b is equal to:

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