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Which of the following is true:

   
   
 

(a) differentiable and continous

 

(d) none of these

 

(c) not differentiable but continous

 

(b) neither differentiable nor continous

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1 Answer

Best answer
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f(x) = $\frac{1}{1-|x|}$

f(x) = { $\frac{1}{1-x}$ , x>=0

           $\frac{1}{1+x}$ , x<0

        }

$\lim_{x\rightarrow 1-}$ = +$\infty$

$\lim_{x\rightarrow 1+}$ = -$\infty$

f(1) = not defined

since LHL $\neq$ RHL $\neq$ f(1) therefore f(x) is not continous at x=1

similiarly you can check for other critical points

P.S: critical points are points where function changes its value abnormally.
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