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Prove that the function If f(x)={:{((x)/...

Prove that the function If `f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" "0", " x=0):}` is not differentiable

A

`(0,infty)`

B

`(-infty, infty) ~ {0}`

C

`(-infty, 0)`

D

`(-infty, infty)`

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The correct Answer is:
B
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. The set of all points, where the function f(x) =x/(1+|x|) is differen...

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  2. The set of points where the function f(x) = x |x| is differentiable i...

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  3. Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" ...

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  4. The set of allpoints of differentiability of the function f(x) ={{:(x^...

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  5. At the point x = 1, the function: f(x) = {{:(x^(3)-1, 1 lt x lt inft...

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  6. Let f(x) = "min" {1, x^(2), x^(3)}, then:

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  7. The function f(x) is defined as: f(x) =1/3 -x, x ,lt 1/3 =(1/3-x)^...

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  8. If f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(,0, x=0):}, then

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  9. Let g(x)=xf(x), where f(x)={{:(x^(2)sin.(1)/(x),":",x ne0),(0,":",x=0)...

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  10. Let f(x)={{:(0,x lt 0),(x^(2),xge0):}, then for all values of x

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  11. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

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  12. The function f (x) = 1+ |sin x| is

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  13. If f(x)={{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

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  14. If x+4|y| = 6y then y as a function of x is

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  15. If f'(x(0)) exists, then lim(h to 0)([f(x(0) +h) -f(x(0) -h))/(2h)) is...

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  16. The function f(x) = {{:(|2x-3|[x], x ge 1),(sin((pix)/2), x lt 1):}

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  17. The function f (x) is defined as under : f(x)={{:(3^(x), -1 le x le...

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  18. A function is defined as follows : f(x) = {{:(x^(3), x^(2) lt 1),(x,...

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  19. The left-hand derivative of f(x) =[x]sin (pix) at k an interger, is:

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  20. If the derivative of the function f(x)={{:(ax^(2)+b,xlt-1),(bx^(2)+a...

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