Home
Class 12
MATHS
Let f(x){{:((x-1)"sin"(1)/(x-1)", "ifx!...

Let `f(x){{:((x-1)"sin"(1)/(x-1)", "ifx!=1),(" 0, "ifx=1.):}`
Then which one of the following is true ?

A

f is differentiable at `x=1` but not at `x=0`

B

f is neither differentiable at `x=0` nor at `x=1`

C

f is differentiable at `x=0` but not at `x=1`

D

f is differentiable at `x=0` but not at `x=1`.

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise Latest Question from AIEEE/JEE Examinations|7 Videos

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise RCQs (Questions from Karnataka CET & COMED)|25 Videos

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise RCQs (Questions from Karnataka CET & COMED)|25 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Recent competitive Questions|10 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise Recent competitive Questions|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x-1/x" then "f'(-1)

The function f(x)=(x-a)"sin"(1)/(x-a) for x!=a and f(a)=0 is :

Let f: R to R be a function defined by : f(x)="Min".{x+1,|x|+1} . Then which of the following is true ?

Let I = int_0^1 (sin x)/(sqrtx) dx and J = int_0^1 (cos x)/(sqrtx) dx . Then which of the following is true?

If f(x) = (x-1)/(x+1) , then f[1/f(x)] =

Observe the following statements A : int (((x^(2)-1)/(x^(2))).e^((x^(2)+1/x)) dx = e^((x^(2)+1)/x) + c R: int f^(')(x).e^(f(x)) dx = f(x) + c Then which of the following is true?

Let f(x)=(x)/(1+x)-log(1+x) , when x gt 0 , then f is :

Let f(x) = ( 2x+1)/(1-3x) , then f^-1 (x) =

MODERN PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -MCQs (LEVEL-II)
  1. If y=(sinx)^cosx, then find (dy)/(dx).

    Text Solution

    |

  2. The function f(x)=(x^(2)-1)|x^(2)-3x+1|+cos(|x|) is not differentiable...

    Text Solution

    |

  3. If y=ce^(x//(x-a)), then 1/y(dy)/(dx) is equal to :

    Text Solution

    |

  4. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

    Text Solution

    |

  5. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

    Text Solution

    |

  6. Derivative of (log x)^(4) is

    Text Solution

    |

  7. If x=e^(y+e^(y+ . . . . .. "to "oo)),xgt0, then (dy)/(dx) is :

    Text Solution

    |

  8. Suppose f(x) is differentiable at x=1 and lim(hto0)(1)/(h)(1+h)=5, the...

    Text Solution

    |

  9. If f is a real valued differentiable function satisfying : |f(x)-f(y...

    Text Solution

    |

  10. If f(x)=||x|-1|, then it is non - derivable at :

    Text Solution

    |

  11. If f:R to T is continuous and differentiable function such that f((1)/...

    Text Solution

    |

  12. If xsiny+ycosx=pi, then the value of y''(0) is :

    Text Solution

    |

  13. The set of points, where f(x)=(x)/(1+|x|) is differentiable, is :

    Text Solution

    |

  14. If x^(m)y^(n)=(x+y)^(m+n), then (dy)/(dx)=

    Text Solution

    |

  15. Let f(x) be differntiable on the interval (0,oo) such that f(1)=1 and ...

    Text Solution

    |

  16. Let f: R to R be a function defined by : f(x)="Min".{x+1,|x|+1}. T...

    Text Solution

    |

  17. Let f(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2,m and n are intgers, m!...

    Text Solution

    |

  18. Let y be an implicit fuction of x defined by : x^(2x)-2x^(x) cot y-1...

    Text Solution

    |

  19. Let f(x){{:((x-1)"sin"(1)/(x-1)", "ifx!=1),(" 0, ...

    Text Solution

    |

  20. Let g(x)=log(f(x)), where f(x) is a twice differentiable positive func...

    Text Solution

    |