The value of limx→a 2−axtan⁡πx2a, is

The value of $lim_{x \to a} {(2 - \frac{a}{x})}^{\tan \frac{π x}{2 a}},$ is

A
$e^{- 1 / π}$
B
$e^{2 / π}$
C
$e^{- 2 / π}$
D
$e^{1 / π}$

Solution:

We have,

$= e^{lim_{h \to 0} - \frac{2}{π} \frac{\frac{π h}{2 a}}{\tan π h / 2 a} (\frac{a}{a + h})} = e^{- 2 / π}$

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