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need solution for RD Sharma maths class 12 chapter 8 Continuity exercise Very short answer question 3

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Answer: 2

Hint: \lim _{x \rightarrow 0} f(x)=f(0)

Given: f(x)=\frac{x}{1-\sqrt{1-x}}

Explanation: We have to findf(0) when f(x) becomes continuous at x = 0


                    \Rightarrow \lim _{x \rightarrow 0} f(x)=f(0)

                    \Rightarrow \lim _{x \rightarrow 0} \frac{x}{1-\sqrt{1-x}}=f(0)

                    Applying L’Hospital rule as the function is in 0/0 form,

                    \begin{aligned} &=>\lim _{x \rightarrow 0} \frac{1}{\frac{-1(-1)}{2 \sqrt{1-x}}}=f(0) \\ &\Rightarrow \lim _{x \rightarrow 0} 2 \sqrt{1-x}=f(0) \\ &\Rightarrow 2 \sqrt{1-0}=f(0) \end{aligned}

                    Hence, f(0)=2

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