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Limits Continuity and Differentiability question

2017 · 9 Apr · Shift 1 · Q39

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JEE Main
Mathematics
Limits Continuity and Differentiability
2017 · 9 Apr · Shift 1 · Q39

Limits Continuity and Differentiability question

2017 · 9 Apr · Shift 1 · Q39

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

The value of k for which the function

f\left( x \right) = \left\{ {\begin{matrix} {{{\left( {{4 \over 5}} \right)}^{{{\tan \,4x} \over {\tan \,5x}}}}\,\,,} & {0 \lt x \lt {\pi \over 2}} \\ {k + {2 \over 5}\,\,\,,} & {x = {\pi \over 2}} \\ \end{matrix} } \right.

is continuous at x =

{\pi \over 2},

is :

A
${{17} \over {20}}$
B
${{2} \over {5}}$
C
${{3} \over {5}}$
D
$-{{2} \over {5}}$

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