Home
Class 12
MATHS
Let f(x)=xsinpix ,x > 0. Then for all na...

Let `f(x)=xsinpix ,x > 0.` Then for all natural numbers `n ,f^(prime)(x)` vanishes at a unique point in the interval `(n , n+1/2)` a unique point in the interval `(n+1/2, n+1)` a unique point in the interval `(n , n+1)` two points in the interval `(n , n+1)`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) vanishes at (A)a unique point in the interval (n , n+1/2) (B)a unique point in the interval (n+1/2, n+1) (C)a unique point in the interval (n , n+1) (D)two points in the interval (n , n+1)

Let x_(n)=(2^(n)+3^(n))^(1//2n) for all natural number n. Then

Let n be a natural and let 'a' be a real number. The number of zeros of x^(2n+1)-(2n+1)x+a=0 in the interval [-1,1] is -

If f(x)=1+x^(m)(x-1)^(n), m , n in N , then f'(x)=0 has atleast one root in the interval

Suppose the function f(x)=x^(n), n ne0 is differentiable for all x. then n can be any element of the interval

the intersection of all the intervals having the form [1+(1)/(n),6,-(2)/(n)], where is a postive integer is

Suppose the function f(x)=x^(n),n!=0 is differentiable for all x. Then n can be any element of the interval

RESONANCE DPP-JEE MAINS-All Questions
  1. If cosx/2dotcosx/(2^2)dotcosx/(2^3)oo=(sinx)/x , then find the value o...

    Text Solution

    |

  2. Differentiate the following function from first principles: e^(-x)

    Text Solution

    |

  3. Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) ...

    Text Solution

    |

  4. Differentiate the following function with respect to x from first prin...

    Text Solution

    |

  5. Ten IIT students and 2 DCE students sit in a row. The number of ways i...

    Text Solution

    |

  6. The function u=e^x sinx , v=e^x cosx satisfy the equation (a) v (du...

    Text Solution

    |

  7. Number of ways in which 7 people can occupy six seats, 3 seats on each...

    Text Solution

    |

  8. Differentiate the following function with respect to x from first prin...

    Text Solution

    |

  9. If y=x+e^x , then (d^2x)/(dy^2) is equal to

    Text Solution

    |

  10. Differentiate the following functions with respect to log(x+sqrt(x^...

    Text Solution

    |

  11. Find the number of ways in which 5A^(prime)sa n d6B ' s can be arrange...

    Text Solution

    |

  12. If u=a x+b ,t h e n(d^n)/(dx^n)(f(a x+b)) is equal to a.(d^n)/(d u^n...

    Text Solution

    |

  13. All the five digit numbers in which each successive digit exceeds its ...

    Text Solution

    |

  14. Evaluate the following limit: (lim)(x->0)(s in3x-s in x)/(sinx)

    Text Solution

    |

  15. If y=sin^(-1)(xsqrt(1-x)+sqrt(x)sqrt(1-x^2)) and (dy)/(dx)=1/(2sqrt(x(...

    Text Solution

    |

  16. The angles of a A B C are in A.P. (order being A, B, C) and it is ...

    Text Solution

    |

  17. Differentiate the following functions with respect to x from first pri...

    Text Solution

    |

  18. If in a triangle A B C , the altitude A M be the bisector of /B A D ,w...

    Text Solution

    |

  19. Differentiate the following functions with respect to x from first pri...

    Text Solution

    |

  20. Differentiate the following functions with respect to x from first...

    Text Solution

    |