The value of `f(0),` so that the function `f(x)=(sqrt(a^2-a x+x^2)-sqrt(a^2+a x+x^2))/(sqrt(a+x)-sqrt(a-x))` becomes continuous for all `x ,` given by `a^(3/2)` (b) `a^(1/2)` (c) `-a^(1/2)` (d) `-a^(3/2)`

Explanation

Given,

`f(x)=(sqrt(a^2-a x+x^2)-sqrt(a^2+a x+x^2))/(sqrt(a+x)-sqrt(a-x))`


f(x) is continuous for all x so it is continuous at `x=0`


`∴f(0)=lim_(x→0​)f(x)`


`=lim_(x→0​)(sqrt(a^2-a x+x^2)-sqrt(a^2+a x+x^2))/(sqrt(a+x)-sqrt(a-x))`
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