The value of `lim_(xtoa) sqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))` is

Options

A. `(5050)/(pie)`
B. `100)/(pie)`
C. `-(5050)/(pie)`
D. `-(4950)/(pie)`

Answer

C

Explanation

`underset(xtoa)limsqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))`
`underset(xtoa)lim(sqrt(a^(2)-x^(2)))/("tan"(pi)/(2)sqrt((a-x)/(a+x)))`
`=(2)/(pi)underset(xtoa)lim((pi)/(2)sqrt((a-x)/(a+x)))/("tan"(pi)/(2)sqrt((a-x)/(a+x)))(a+x)=(4a)/(pi)`