Home
Class 12
MATHS
If lim(t to a) (int(a)^(t) f(t)dt-(t-a)/...

If `lim_(t to a) (int_(a)^(t) f(t)dt-(t-a)/2 (f(t) -f(a)))/(t-a)^(3)= 0`, then maximum degree of `f(x)` is:

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ML KHANNA|Exercise ProblemSet (2) Fill in the blanks|1 Videos

  • DEFINITE INTEGRAL

    ML KHANNA|Exercise Problem set (3) (Multiple Choice Questions)|38 Videos

  • DEFINITE INTEGRAL

    ML KHANNA|Exercise ProblemSet (1) True and false|1 Videos

  • CORRELATION AND REGRESSION

    ML KHANNA|Exercise SELF ASSESSMENT TEST |10 Videos

  • DETERMINANTS

    ML KHANNA|Exercise Self Assessment Test |19 Videos

Similar Questions

Explore conceptually related problems

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

lim_(x to 0)(int_(-x)^(x) f(t)dt)/(int_(0)^(2x) f(t+4)dt) is equal to

If f(-x)+f(x)=0 then int_(a)^(x)f(t)dt is

Evaluate lim_(x rarr4)int_(4)^(x)((4t-f(t)))/((x-4))dt

If f(x)=int_(1)^(x)(ln t)/(1+t)dt, then

Let f be a function defined on the interval [0,2pi] such that int_(0)^(x)(f^(')(t)-sin2t)dt=int_(x)^(0)f(t)tantdt and f(0)=1 . Then the maximum value of f(x) is…………………..

If int_(0)^(1) f(t)dt=x^2+int_(0)^(1) t^2f(t)dt , then f'(1/2)is

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

ML KHANNA-DEFINITE INTEGRAL-ProblemSet (2) (Multiple Choice Questions)
  1. int(0)^(pi) x f (sin x)dx=

    Text Solution

    |

  2. Evaluate int0 ^oo log(x+1/x) dx / (1+x^2)

    Text Solution

    |

  3. int(0)^(pi//2) [2log sin x-log sin 2x] dx=

    Text Solution

    |

  4. If int(0)^(pi) x f(sin x)dx= k int(0)^(pi//2) f(sin x) dx then the val...

    Text Solution

    |

  5. For n gt 0 int(0)^(2pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= ….

    Text Solution

    |

  6. int(0)^(pi//2) (sin^(2)x)/(sin x+cos x) dx is equal to

    Text Solution

    |

  7. The value of the integral int(0)^(1) x (1-x)^(n) dx is

    Text Solution

    |

  8. If int(0)^(1) x^(m) (1-x)^(n) dx= R int(0)^(1) x^(n) (1-x)^(m) dx, the...

    Text Solution

    |

  9. If I= int(0)^(1) (e^(t))/(1+t) dt, then p= int(0)^(1) e^(t) log (1+t) ...

    Text Solution

    |

  10. int(0)^(pi//2n) (dx)/(1+ cot^(n) nx) is equal to

    Text Solution

    |

  11. The value of the integral underset(0)overset(1)int cot^(-1) (1-x+x^...

    Text Solution

    |

  12. int(0)^(1) tan^(-1) (1-x+x^(2)) dx=

    Text Solution

    |

  13. int(0)^(pi//2) (cos x dx)/(1+ cos x +sin x)=

    Text Solution

    |

  14. Let I= int(0)^(pi//2) (dx)/(1+sin x') then int(0)^(pi) (x^(2) cos x)/(...

    Text Solution

    |

  15. a(n) = int(0)^(pi//2) (sin^(2) nx)/(sin x)dx, then a(2)-a(1), a(3)-a(2...

    Text Solution

    |

  16. If f(x) and g(x) are continuous functions satisfying f(x)= f(a-x) and ...

    Text Solution

    |

  17. If f (x) is monotonic differentiable function on [a,b] then int(a)^(b)...

    Text Solution

    |

  18. Let T >0 be a fixed real number. Suppose f is continuous function such...

    Text Solution

    |

  19. If lim(t to a) (int(a)^(t) f(t)dt-(t-a)/2 (f(t) -f(a)))/(t-a)^(3)= 0, ...

    Text Solution

    |

  20. If f(y)= e^(y), g(y)= y, y gt 0 and F(t) = int(0)^(t) f(t-y) g(y) dy, ...

    Text Solution

    |