Home
Class 11
MATHS
Newton-Leinbnitz's formula states that d...

Newton-Leinbnitz's formula states that `d/dx(int_(phi(x))^(psi(x)) f(t)dt)=f(psi(x)){d/dxpsi(x)}-f(phi(x)){d/dxphi(x)}`
Answer the following questions based on above passage:
If `lim_(xrarr0)int_0^(x) (t^2dt)/((x-sinx)sqrt(a+t))=1`, then the value of a is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Newton-Leinbnitz's formula states that d/dx(int_(phi(x))^(psi(x)) f(t)dt)=f(psi(x)){d/dxpsi(x)}-f(phi(x)){d/dxphi(x)} Answer the following questions based on above passage: lim_(xrarr0)int_0^(x^2) ((cost)^2dt)/((xsinx))=

Newton-Leinbnitz's formula states that d/dx(int_(phi(x))^(psi(x)) f(t)dt)=f(psi(x)){d/dxpsi(x)}-f(phi(x)){d/dxphi(x)} Answer the following questions based on above passage: Let f(x) be a differentiable function and f(1)=2, If lim_(xrarr1)int_2^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is equal to

The value of lim_(xrarr0)(int_0^(x^2) cos(t^2)dt)/(xsinx) is

Evaluate lim_(xrarr0)(x-int_0^(x) cost^2dt)/(x^3-6x)

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

The value of lim_( x to 0) (int_(0)^(x^(2)) cos(t^(2))dt)/(x sinx) is

If int_(0)^(x) f(t)dt=x+int_(x)^(1)t f(t)dt , find the value of f(1).

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

if int_0^(x^2(1+x))f(t)dt=x then the value of 10f(2) must be

The value of lim_(x to 0)(int_(0)^(x^(2))sec^(2)t dt)/(x sin x) is equal to -

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f be a polynomial function such that f(x) f(y) + 2 = f(x) + f(y) +...

    Text Solution

    |

  2. Newton-Leinbnitz's formula states that d/dx(int(phi(x))^(psi(x)) f(t)d...

    Text Solution

    |

  3. Newton-Leinbnitz's formula states that d/dx(int(phi(x))^(psi(x)) f(t)d...

    Text Solution

    |

  4. Newton-Leinbnitz's formula states that d/dx(int(phi(x))^(psi(x)) f(t)d...

    Text Solution

    |

  5. f(x) is not differentiable at x=c if either Lf'( c )neRf'( c ) [if the...

    Text Solution

    |

  6. If f(x)={(x[x], 0lexlt2),((x-1)[x],2lexle3):}, then f(x) is

    Text Solution

    |

  7. f(x) is not differentiable at x=c if either Lf'( c )neRf'( c ) [if the...

    Text Solution

    |

  8. Let f(x) be a polynomial satisfying f(0)=2, f'(0)=3 and f''(x)=f(x). A...

    Text Solution

    |

  9. Match List - I with List-II

    Text Solution

    |

  10. If [x] denotes greatest integer le x, then match the following limits ...

    Text Solution

    |

  11. Match List - I with List-II

    Text Solution

    |

  12. The value of lim(xrarr1)(x+x^2+x^3+...+x^97-97)/((x-1)) must be M. The...

    Text Solution

    |

  13. If lim(xrarr0)1/x^2(e^(ax)-e^x-x)=3/2, then the value of |alpha|must b...

    Text Solution

    |

  14. If f(x)={(((1-sin^3x))/(3cos^2x), x lt pi/2), (a, x=pi/2), ((b(1-sinx)...

    Text Solution

    |

  15. Given, f(x)={((x^4-256)/(x-4), x ne 4), ( lambda, x = 4):}. If f is co...

    Text Solution

    |

  16. If f(x)={((8^x-4^x-2^x+1^x)/x^2, x gt 0),(e^x sinx + pi x + lambda In4...

    Text Solution

    |

  17. If f(x)={(((exp{(x+3)ln27})^(1/27[x])-9)/(3^x-27), x lt 3), (lamda.((1...

    Text Solution

    |

  18. If f(x)={(5+x^2, x lt 1), (x-4, x ge 1):} is jump discontinuous, then ...

    Text Solution

    |

  19. A function f : R to R satisfies the equation f(x + y) = f(x), f(y) for...

    Text Solution

    |

  20. If f(x) is continuous and f(9/2) = 2/9, then find lim(xrarr0)9f((1-cos...

    Text Solution

    |