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Let $f : \mathbb{R} \to \mathbb{R}$ be a function defined as
$$f(x) = \begin{cases} \dfrac{\sin(a+1)x + \sin 2x}{2x}, & \text{if } x < 0 \ b, & \text{if } x = 0 \ \dfrac{\sqrt{x + bx^2} - \sqrt{x}}{bx^{3/2}}, & \text{if } x > 0 \end{cases}$$
If $f$ is continuous at $x = 0$, then the value of $a + b$ is equal to:
(1) $-\dfrac{5}{2}$
(2) $-2$
(3) $-3$
(4) $-\dfrac{3}{2}$
BETA
