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Limits Continuity and Differentiability question

2019 · 10 Apr · Shift 1 · Q31

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JEE Main
Mathematics
Limits Continuity and Differentiability
2019 · 10 Apr · Shift 1 · Q31

Limits Continuity and Differentiability question

2019 · 10 Apr · Shift 1 · Q31

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If

f(x) = \left\{ {\begin{matrix} {{{\sin (p + 1)x + \sin x} \over x}} & {,x \lt 0} \\ q & {,x = 0} \\ {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{\frac{3}{2}}}}}} & {,x \gt 0} \\ \end{matrix} } \right.

is continuous at x = 0, then the ordered pair (p, q) is equal to

A
$\left( { - {3 \over 2}, - {1 \over 2}} \right)$
B
$\left( { - {1 \over 2},{3 \over 2}} \right)$
C
$\left( { - {3 \over 2}, {1 \over 2}} \right)$
D
$\left( { {5 \over 2}, {1 \over 2}} \right)$

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