If f(x)=xe−1|x|+1x,x≠00,x=0 then f is 

If f(x)=xe1|x|+1x,x00,x=0 then f is 

  1. A

    discontinuous everywhere

  2. B

    continuous and  differentiable at x=0

  3. C

    differentiable everywhere

  4. D

    continuous but not differentiable at x= 0

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    Solution:

    f(x)=xx<0xe2xx>00x=0

    f is clearly a continuous function

            f(x)=1,x<0e2x+2xe2x,x>0limh0f(0+h)f(0)h=limh0hh=1limh0+f(0+h)f(0)h=limh0+he2hh=limh0+e2h=0

    f is not differentiable at x = 0.

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