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Limits Continuity and Differentiability question

2021 · 26 Feb · Shift 2 · Q36

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 26 Feb · Shift 2 · Q36

Limits Continuity and Differentiability question

2021 · 26 Feb · Shift 2 · Q36

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

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

be defined as

f(x) = \left\{ \begin{array}{ll} 2\sin\left(-\dfrac{\pi x}{2}\right) & \text{if } x \lt -1 \\ |ax^2 + x + b| & \text{if } -1 \le x \le 1 \\ \sin(\pi x) & \text{if } x \gt 1 \end{array} \right.

If

f(x)

is continuous on

\mathbb{R}

, then

a + b

equals :

A
$-$ 3
B
3
C
$-$ 1
D
1

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