Home
Class 12
MATHS
The value of lim(a rarr oo)(1)/(a^(2))in...

The value of `lim_(a rarr oo)(1)/(a^(2))int_(0)^(a)ln(1+e^(x))dx` equals

A

`0`

B

`1`

C

`1/2`

D

non-existent

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 1 Part-III|2 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - 1|30 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 1|31 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

Let a in(0,(pi)/(2)) ,then the value of lim_(a rarr0)(1)/(a^(3))int_(0)^(a)ln(1+tan a tan x)dx is equal to

lim_(n rarr oo)(n)/(2^(n))int_(0)^(2)x^(n)dx equals

The value of lim_(x rarr oo)((ln x)^(2))/(x^(2)) is

The value of (lim_(x rarr0)(1)/(x^(6))int_(0)^(x^(2))sin(t^(2))dt) is equal to

The value of lim_(x rarr oo)x^(2)ln(x cot^(-1)x) is

lim_(x rarr0)(1)/(x^(2))int_(0)^(x)(tdt)/(t^(4)+1) is equal to

If a,b and c are real numbers then the value of lim_(t rarr0)ln((1)/(t)int_(0)^(t)(1+a sin bx)^((c)/(x))dx) equals

The value of lim_(x rarr0)(int_(0)^(x) xe^(t^(2))dt)/(1+x-e^(x)) is equal to

The value of lim_(x rarr0)int_(0)^(x)(t ln(1+t))/(t^(4)+4)dt

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1 Part-II
  1. If int(a)^(y)cost^(2)dt = int(a)^(x^(2))(sint)/(t) dt, then the value ...

    Text Solution

    |

  2. If int(sinx)^(1)t^(2) (f(t)) dt = (1-sinx), then f ((1)/(sqrt(3))) is

    Text Solution

    |

  3. The value of lim(a rarr oo)(1)/(a^(2))int(0)^(a)ln(1+e^(x))dx equals

    Text Solution

    |

  4. f(x) = underset(1)overset(sinxcosy)int(y^(2)+y+1)dy, then

    Text Solution

    |

  5. int(0)^(pi//2) sin^(4)xcos^(3)dx is equal to :

    Text Solution

    |

  6. int(0)^(1)x^(2)(1-x)^(3)dx is equal to

    Text Solution

    |

  7. Let I = int(1)^(3)sqrt(x^(4)+x^(2)), dx then

    Text Solution

    |

  8. I=int0^(2pi) e^(sin^2x+sinx+1)dx then

    Text Solution

    |

  9. Let f"'(x)>=0 ,f'(x)> 0, f(0) =3 & f(x) is defined in [-2, 2].If f(x) ...

    Text Solution

    |

  10. Let mean value of f(x) = 1/(x+c) over interval (0,2) is 1/2 ln 3 then...

    Text Solution

    |

  11. lim(nrarr0) sum(r=1)^(n) ((r^(3))/(r^(4)+n^(4))) equals to :

    Text Solution

    |

  12. underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-...

    Text Solution

    |

  13. lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

    Text Solution

    |

  14. lim(nrarroo) [sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))/(n)pi] i...

    Text Solution

    |

  15. Let I(n) = int(0)^(1)(1-x^(3))^(n)dx, (nin N) then

    Text Solution

    |

  16. The area bounded by the x-axis and the curve y = 4x - x^2 - 3 is

    Text Solution

    |

  17. The area of the figure bounded by right of the line y = x + 1, y= cos ...

    Text Solution

    |

  18. Area bounded by curve y^(3) - 9y + x = 0, and y-axis is

    Text Solution

    |

  19. Let f"[0,oo)rarr R be a continuous and stricity increasing function s...

    Text Solution

    |

  20. The area bounded by the curve y = e^x & the lines y = |x-1|, x = 2 is...

    Text Solution

    |