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Question
Find f (0), so that \[f\left( x \right) = \frac{x}{1 - \sqrt{1 - x}}\] becomes continuous at x = 0.
Solution
Given:
\[\Rightarrow f\left( x \right) = \frac{x\left( 1 + \sqrt{1 - x} \right)}{\left( 1 - \sqrt{1 - x} \right)\left( 1 + \sqrt{1 - x} \right)}\]
\[ \Rightarrow f\left( x \right) = \frac{x\left( 1 + \sqrt{1 - x} \right)}{1 - \left( 1 - x \right)}\]
\[ \Rightarrow f\left( x \right) = \left( 1 + \sqrt{1 - x} \right)\]
So, for
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