Home
Class 12
MATHS
If f(x)=prod(n=1)^(100)(x-n)^(n(101-n));...

If `f(x)=prod_(n=1)^(100)(x-n)^(n(101-n))`; then `(f(101))/(f'(101))=`

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

The sum of the series (.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100)) is "____" .

If f(x)=x^3-x^2+100x+2002 ,t h e n a) f(1000)>f(1001) b) f(1/(2000))>f(1/(2001)) c) f(x-1)>f(x-2) d) f(2x-3)>f(2x)

If int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C then f(x) is (A) 1+x^n (B) 1+x^-n (C) x^n+x^-n (D) x^n-x^-n

The total number of different terms in the product (.^(101)C_(0) - .^(101)C_(1)x+.^(101)C_(2)x^(2)-"….."-.^(101)C_(101)x^(101))(1+x+x^(2)+"…."+x^(100))^(101) is "____" .

Prove that: sum_(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)

If f(x)=(1+x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+(f^(''')(0))/(3!)+......(f^n(0))/(n !)dot

If phi(x)=lim_(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n)) , then

If f(x+1)+f(x-1)=2f(x) and f(0)=0, then find f(n),n in N , is

The coefficient of x^(50) in (x+^(101)C_(0))(x+^(101)C_(1)).....(x+^(101)C_(50)) is

If f(x)=lim_(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal to

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f(x)=[tanx[cotx]], x in [(pi)/(12),(pi)/(2)), (where [.] denotes t...

    Text Solution

    |

  2. Let f[-2,2]rarrR be a continuous function such that f(x)assumes only i...

    Text Solution

    |

  3. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)); then (f(101))/(f'(101))=

    Text Solution

    |

  4. A curve in the xy-plane is parametrically given by x=t+t^3a n dy=t^2,w...

    Text Solution

    |

  5. Number of points of discontinuity of f(x)=[sin^(-1)x]-[x] in its domai...

    Text Solution

    |

  6. If g(x)=(lim)(mtooo)(x^mf(x)+h(x)+3)/(2x^m+4x+1) when x!=1a n dg(1)=e^...

    Text Solution

    |

  7. Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable...

    Text Solution

    |

  8. If f(x)=|[(x-a)^4, (x-a)^3, 1] , [(x-b)^4, (x-b)^3,1] , [(x-c)^4, (x-c...

    Text Solution

    |

  9. Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real xa n dydot If f(x) is ...

    Text Solution

    |

  10. A function f: R -> R satisfies the equation f(x)f(y)-f(x y)=x+yAAx ,y ...

    Text Solution

    |

  11. Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in ...

    Text Solution

    |

  12. Let f(x)=(g(x))/x when x!=0 and f(0)=0. If g(0)=g^(prime)(0)=0and g...

    Text Solution

    |

  13. Let f(x+y)=f(x)+f(y)+2x y-1 for all real xa n dy and f(x) be a differe...

    Text Solution

    |

  14. Let f:(-oo,oo) -> [0,oo) be a continuous function such that f(x+y)=f(x...

    Text Solution

    |

  15. The function f(x) is discontinuous only at x = 0 such that f^(2)(x)=1 ...

    Text Solution

    |

  16. f(x)={(x^2+e^(1/(2-x)))^(-1), x!=2 k ,x=2 is continuous from right at ...

    Text Solution

    |

  17. The derivative of the function represented parametrically as x=2t=|...

    Text Solution

    |

  18. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

    Text Solution

    |

  19. If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuou...

    Text Solution

    |

  20. Find the set of points where the following functions are discontinuous...

    Text Solution

    |