Home
Class 12
MATHS
The left hand derivative of f(x)=[x]sin...

The left hand derivative of `f(x)=[x]sin(pix)` at `x = k`, `k` is an integer, is

A

`(-1)^(k) (k - 1)pi`

B

`(-1)^(k-1)(k-1)pi`

C

`(-1)^(k) kpi`

D

`(-1)^(k-1) kpi`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|6 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

The left hand derivative of f(x)=[x]sin(pi x) at x=k,k is an integer,is

If the right hand derivative of f(x)=[x]tan pi x at x=7 is k pi then k=

The derivative of f(x)=(8^(x))/(sin x)

The left hand limit of the function f(x)=4

Find the right hand derivative and the left hand derivative of f(x)=x-1,x =2 at the point x=2 and hence show that f(x) is not differentiable at x=2 .

Find the derivative of f(x)=k at x=0 and x=2.

The ratio of left hand derivative and right hand derivative of the function f(x)=[x]tan pi x ,where [. ] is G.I.F.,at x=pi is given by

Find the left and right hand derivative of the following function at given point: f(x)=e^(-|x|)a t\ x=0

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. For every pair of continuous functions f,g:[0,1]->R such that max{f(x)...

    Text Solution

    |

  2. Let f:R-> R and g:R-> R be respectively given by f(x) = |x| +1 and g...

    Text Solution

    |

  3. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

    Text Solution

    |

  4. Q. For every integer n, let an and bn be real numbers. Let function f:...

    Text Solution

    |

  5. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

    Text Solution

    |

  6. "If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le ...

    Text Solution

    |

  7. For the fucntion f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  8. Let g(x) = ((x -1)^(n))/(log cos^(m)(x-1)),0 lt x lt 2, m and n are in...

    Text Solution

    |

  9. Let f and g be real valued functions defined on interval (-1, 1) such ...

    Text Solution

    |

  10. In the following, [x] denotes the greatest integer less than or equal ...

    Text Solution

    |

  11. If f(x)=min.(1,x^2,x^3), then

    Text Solution

    |

  12. Let f(x) = ||x|-1|, then points where, f(x) is not differentiable is/a...

    Text Solution

    |

  13. lff is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, t...

    Text Solution

    |

  14. The domain of the derivative of the function f(x)={t a n^(-1)x ,if|x|l...

    Text Solution

    |

  15. The left hand derivative of f(x)=[x]sin(pix) at x = k, k is an intege...

    Text Solution

    |

  16. Which of the following functions is differentiable at x = 0? cos (|x|...

    Text Solution

    |

  17. For x in R, f(x) = | log 2- sin x| and g(x) = f(f(x)), then

    Text Solution

    |

  18. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

    Text Solution

    |

  19. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  20. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |