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Find f(0) , so that f(x)=x/(1-sqrt(1-x))...

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

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To find \( f(0) \) such that the function \( f(x) = \frac{x}{1 - \sqrt{1 - x}} \) is continuous at \( x = 0 \), we need to evaluate the limit of \( f(x) \) as \( x \) approaches 0. ### Step-by-Step Solution: 1. **Evaluate the limit as \( x \) approaches 0:** \[ \lim_{x \to 0} f(x) = \lim_{x \to 0} \frac{x}{1 - \sqrt{1 - x}} \] ...
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RD SHARMA-CONTINUITY-Solved Examples And Exercises
  1. Define continuity of a function at a point.

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  2. What happens to a function f(x) at x=a , if (lim)(x->a)f(x)=f(a)

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

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  18. Let f(x)={(x-4)/(|x-4|)+a ,x<4a+b ,(x-4)/(|x-4|)+b ,x >4 Then f(x) is...

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  20. Let f(x)=|x|+|x-1|, then (a)f(x) is continuous at x=0, as well at ...

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