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Limits Continuity and Differentiability question

2021 · 27 Jul · Shift 1 · Q32

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 27 Jul · Shift 1 · Q32

Limits Continuity and Differentiability question

2021 · 27 Jul · Shift 1 · Q32

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f:\left( { - {\pi \over 4},{\pi \over 4}} \right) \to R

be defined as

f(x) = \left\{ {\begin{matrix} {{{(1 + |\sin x|)}^{{{3a} \over {|\sin x|}}}}} & , & { - {\pi \over 4} \lt x \lt 0} \\ b & , & {x = 0} \\ {{e^{\cot 4x/\cot 2x}}} & , & {0 \lt x \lt {\pi \over 4}} \\ \end{matrix} } \right.

If f is continuous at x = 0, then the value of 6a + b2 is equal to :

A
1 $-$ e
B
e $-$ 1
C
1 + e
D
e

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