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Limits Continuity and Differentiability question

2011 · Shift 2 · Q33

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2011 · Shift 2 · Q33

Limits Continuity and Differentiability question

2011 · Shift 2 · Q33

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMCQ+3 / −1

If

\mathop {\lim }\limits_{x \to 0} {[1 + x\ln (1 + {b^2})]^{1/x}} = 2b{\sin ^2}\theta

,

b \gt 0

and

\theta \in ( - \pi ,\pi ]

, then the value of

\theta

is

A
$\pm {\pi \over 4}$
B
$\pm {\pi \over 3}$
C
$\pm {\pi \over 6}$
D
$\pm {\pi \over 2}$

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