The value of f(0), so that the function f(x) = (√(a^2-ax+x^2)-√(a^2+ax+x^2))/(√(a+x)-√(a-x)) becomes continuous for all x, given by : ​

Question

The value of f(0), so that the function f(x) = \(\frac{\sqrt{a^2-ax+x^2}-\sqrt{a^2+ax+x^2}}{\sqrt{a+x}-\sqrt{a-x}}\) becomes continuous for all x, given by :

A. a^3/2 

B. a^1/2 

C. –a^1/2 

D. –a^3/2

Answer 1

Option : (C)

(i) A function f(x) is said to be continuous at a point x = a of its domain, if 

 \(\lim\limits_{x \to a}f(x)\) = f(a)

 \(\lim\limits_{x \to a^+}f(a+h)\) = \(\lim\limits_{x \to a^-}f(a-h)\) = f(a)

f(x) = \(\frac{\sqrt{a^2-ax+x^2}-\sqrt{a^2+ax+x^2}}{\sqrt{a+x}-\sqrt{a-x}}\) 

Using rationalization method,