Home
Class 12
MATHS
If f is an even function such that (lim)...

If `f` is an even function such that `(lim)_(hvec0)(f(h)-f(0))/h` has some finite non-zero value, then prove that `f(x)` is not differentiable at `x=0.`

A

f is continuous and derivable at x = 0

B

f is continuous but not derivable at x = 0

C

f may be discontinuous at x = 0

D

None of these

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 2 (Level-I) Objective Problems | JEE Main|15 Videos

  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 2 (Level-II) Multiple Correct | JEE Advanced|8 Videos

  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|15 Videos

  • DETERMINANTS

    MOTION|Exercise EXERCISE-4 (LEVEL-II)|6 Videos

  • DIFFERENTIAL EQUATION

    MOTION|Exercise Exercise 4|29 Videos

Similar Questions

Explore conceptually related problems

If f is an even function such that lim_(h rarr0)(f(h)-f(0))/(h) has some finite non-zero value,then prove that f(x) is not differentiable at x=0.

If f is an even function, prove that lim_(xto0^(-)) (x)=lim_(xto0^(+)) f(x).

Which of the function is non-differential at x=0?f(x)=x|x|

If an even function f is differentiable at x=0, then f '(0)=

If f(x) is a differentiable function of x then lim_(h rarr0)(f(x+3h)-f(x-2h))/(h)=

If f is an even function,then prove that lim_(x rarr0^(-))f(x)=lim_(x rarr0^(+))f(x)

If f is derivable function of x, then underset(hto0)("lim")(f(x+h)-f(x-h))/(h)=

the value of lim_(h to 0) (f(x+h)+f(x-h))/h is equal to

Let f(x) be a real valued function such that f(a)=0. If g(x)=(x-a)f(x) is continuous but notdifferentiable at x=a and h(x)=(x-a)^(2)f(x) is continuous and differentiable at x=a .Then f(x)

Which of the function is non-differential at x=0?f(x)=cos|x|

MOTION-DIFFERENTIABILITY-Exercise - 1 Objective Problems | JEE Main
  1. if f(x) = x( sqrtx + sqrt(x+1)), then

    Text Solution

    |

  2. Let f (x)= [{:((x(3e^(1//x)+4))/(2 -e^(1//x)),,,( x ne 0)),(0 ,,, x=0)...

    Text Solution

    |

  3. If f(x)=x/(sqrt(x+1)-sqrtx) be a real valued function, then

    Text Solution

    |

  4. If f(x)=[tan^(2)x] then (where [ast] denotes the greatest integer func...

    Text Solution

    |

  5. Let f(x) be defined in [-2,2] by f(x) = { max(sqrt4-x^2),sqrt(1+x^2)),...

    Text Solution

    |

  6. The function f(x)=sin^(-1)(cosx) is

    Text Solution

    |

  7. Let f(x)=(abs(x))/(sinx) for xne0 "and" f(0)=1 "then",

    Text Solution

    |

  8. If f(x) = [x^2] + sqrt({x}^2, where [] and {.} denote the greatest int...

    Text Solution

    |

  9. If f(x)=a|sinx|+be^|x|+c|x|^3 and if f(x) is differentiable at x=0 the...

    Text Solution

    |

  10. If f(x) is differentiable everywhere, then which one of the following ...

    Text Solution

    |

  11. Let f(x+y)=f(x)*f(y)AAx , y in R,suppose that f(3)=3 and f^(prime)(0...

    Text Solution

    |

  12. LEt F: R->R is a differntiable function f(x+2y) =f(x) + f(2y) +4xy for...

    Text Solution

    |

  13. Suppose that f is a differentiable function with the property that f(x...

    Text Solution

    |

  14. "Let" f(x+y)=f(x)f(y) "for all x,y, where" f(0)ne0. If f'(0)=2, then f...

    Text Solution

    |

  15. The functions defined by f(x)="max" {x^(2),(x-1)^(2),2x(1-x)}, 0lexle1

    Text Solution

    |

  16. If f is an even function such that (lim)(hvec0)(f(h)-f(0))/h has some ...

    Text Solution

    |

  17. Let f: R to R be a function defined byf(x)="min" {x+1,|x|+1}. Then, wh...

    Text Solution

    |