Find f (0), so that f(x) = x/1-√(1-x) becomes continuous at x = 0. ​

Question

Find f (0), so that f(x) = \(\frac{x}{1-\sqrt{1-x}}\) becomes continuous at x = 0.

Answer 1

Formula :- 

(i) If f(x) is continuous at x = 0 then,  
\(\lim\limits_{x \to a}f(x)\) = f(a)

Given :-

f(x) = \(\frac{x}{1-\sqrt{1-x}}\)

Using rationalization method with 1 + \(\sqrt{1-x}\)

For function to be continuous at x = 0
\(\lim\limits_{x \to 0}(1+\sqrt{1-x})\) = f(0)

f(0) = 2 

the function f(x) become continuous at x = 0