Home
Class 12
MATHS
Let f: R to R satisfies |f(x)|lex^(2)A...

Let f: `R to R` satisfies `|f(x)|lex^(2)AAx in R.` then show thata f(x) is differentiable at x=0

A

f' is continuous but non-differentiable at x = 0

B

‘f ’ is discontinuous at x = 0

C

‘f ’ is differentiable at x = 0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL 2|103 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R , then show that f(x) is differentiable at x = 0.

If f(3x+2)+f(3x+29)=0 AAx in R , then the period of f(x) is

Let f: R->R satisfying |f(x)|lt=x^2,AAx in R be differentiable at x=0. Then find f^(prime)(0)dot

Let f: Rvec satisfying |f(x)|lt=x^2AAx in R be differentiable at x=0. The find f^(prime)(0)dot

Let f:[-1,1] to R_(f) be a function defined by f(x)=(x)/(x+2) . Show that f is invertible.

Let f: R to R be a function defined as f (x) = 3x+ 7 , x in R . Show that f is an onto functions.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

f:R-{0} to R is defined as f(x)=x+1/x then show that (f(x))^(2)=f(x^(2))+f(1)

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL -1
  1. Let f(x) = lambda + mu|x| + v |x|^(2) " where " lambda, mu, v are re...

    Text Solution

    |

  2. Let f(x) be a function defined by f(x)={{:(,e^(x),x lt 2),(,a+bx,x ge ...

    Text Solution

    |

  3. Let f: R to R satisfies |f(x)|lex^(2)AAx in R. then show thata f(x)...

    Text Solution

    |

  4. f(x)=[sinx]+[cosx] ,x epsilon [0,2pi], where[.] denotes the greatest ...

    Text Solution

    |

  5. Discuss the continuity of the function f(x) = underset(n rarr oo)(lim)...

    Text Solution

    |

  6. If a function f : [-2a, 2a] rarr R is an odd function such that f(x) =...

    Text Solution

    |

  7. Let f(x+y) = f(x) f(y) and f(x) = 1 + x g(x) G(x) where lim(x->0) g(x)...

    Text Solution

    |

  8. Let f(x) be a continuous defined for 1le xle 3. if f(x) takes ra...

    Text Solution

    |

  9. Let f(x) = [ n + p sin x], x in (0,pi), n in Z, p is a prime number an...

    Text Solution

    |

  10. f(x)=min{1,cosx,1-sinx},-pilexlepi, then

    Text Solution

    |

  11. A function f(x) is defined in the interval [1,4) as follows f(x)={{:(,...

    Text Solution

    |

  12. Discuss the continuity of f(x)=(lim)(n->oo)(x^(2n)-1)/(x^(2n)+1)

    Text Solution

    |

  13. Discuss the continuity of function f(x)={{:(1,"if x is rational"),(...

    Text Solution

    |

  14. Let f(x)={(tan^(-1)x, , |x|ge1),((x^(2)-1)/4, , |x|lt1):} then domain ...

    Text Solution

    |

  15. No. of points of discontinuity of [ 2 x^3 - 5] in [1,2] is

    Text Solution

    |

  16. Discuss the differentiability of f(x)=m a x{2sinx ,1-cosx}AAx in (0,...

    Text Solution

    |

  17. Let f(x)= {{:((x)/(1+|x|)",", |x| ge1), ((x)/(1-|x|)",", |x| lt 1):},...

    Text Solution

    |

  18. Let y=tan((pi)/4+x/2). Then (dy)/(dx) at x=(pi)/4

    Text Solution

    |

  19. Let f(x) = lim( n to oo) m ( sin x)^(2n) then which of the follow...

    Text Solution

    |

  20. If f is a periodic function then

    Text Solution

    |