The value of k for which the function f ( x ) = ( 4 5 )^ ,4x ,5x … - Vidyadip

MCQ

The value of $k$ for which the function $f\left( x \right) = \left\{ \begin{gathered} {\left( {\frac{4}{5}} \right)^{\frac{{\tan \,4x}}{{\tan \,5x}}}},\,\,\,\,0 < x < \frac{\pi }{2} \hfill \\ k + \frac{2}{5}\,\,\,,\,\,\,\,\,\,\,\,\,\,\,x = \frac{\pi }{2} \hfill \\ \end{gathered} \right.$ is continuous at $x\,= \frac{\pi}{2}$ is

A
$\frac{17}{20}$
B
$\frac{2}{5}$
✓
$\frac{3}{5}$
D
$-\frac{2}{5}$

✓

Answer

Correct option: C.

$\frac{3}{5}$

c
$\mathop {\lim }\limits_{x \to \pi /2} f\left( x \right) = f\left( {\pi /2} \right)$

$k + 2/5 = 1$

$k = 1 - \frac{2}{5}$

$k = \frac{3}{5}$

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