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Limits Continuity and Differentiability question

2021 · 18 Mar · Shift 2 · Q29

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 18 Mar · Shift 2 · Q29

Limits Continuity and Differentiability question

2021 · 18 Mar · Shift 2 · Q29

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f : \mathbb{R} \to \mathbb{R}

be a function defined as

f(x) = \left\{ \begin{array}{ll} \dfrac{\sin(a+1)x + \sin 2x}{2x} & \text{if } x \lt 0 \\ b & \text{if } x = 0 \\ \dfrac{\sqrt{x + bx^3} - \sqrt{x}}{bx^{5/2}} & \text{if } x \gt 0 \end{array} \right.

If

f

is continuous at

x = 0

, then the value of

a + b

is equal to :

A
$-$ 3
B
$-$ 2
C
$- {5 \over 2}$
D
$- {3 \over 2}$

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