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Limits Continuity and Differentiability question

2021 · 31 Aug · Shift 1 · Q33

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 31 Aug · Shift 1 · Q33

Limits Continuity and Differentiability question

2021 · 31 Aug · Shift 1 · Q33

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If the function

f(x) = \left\{ {\begin{matrix} {{1 \over x}{{\log }_e}\left( {{{1 + {x \over a}} \over {1 - {x \over b}}}} \right)} & , & {x \lt 0} \\ k & , & {x = 0} \\ {{{{{\cos }^2}x - {{\sin }^2}x - 1} \over {\sqrt {{x^2} + 1} - 1}}} & , & {x \gt 0} \\ \end{matrix} } \right.

is continuous at x = 0, then

{1 \over a} + {1 \over b} + {4 \over k}

is equal to :

A
$-$ 5
B
5
C
$-$ 4
D
4

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