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 ENGLISH|Exercise Exercise 1 Part-III|1 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - 1|29 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 1|64 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr oo)(log(1+x))/(x)

lim_(x rarr oo)((log x)/(x^(n)))

int_(0)^(1)x log (1+2 x)dx

1. int_(0)^(oo)e^(-x/2)dx

int_(1)^(4) log_(e)[x]dx equals

lim_(x rarr oo)((log x)/(x))^(1/x)

The value of lim_(x rarr 0) (1-cos2x)/(e^(x^(2))-e^(x)+x) is

lim_(x rarr oo){((log x)^(3))/(x)}

The value of int_(log1//2)^(log2)sin{(e^(x)-1)/(e^(x)+1)}dx is equal to

The value of lim_(x rarr0)(2int_(0)^(cos x ) cos^(-1) (t))/(2x- sin 2 x)dx is

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1 Part-II
  1. If int(0)^(y)cost^(2)dt=int(0)^(x^(2))(sint)/tdt, then prove that (dy)...

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Let f(x) = secx*f'(x), f(0) = 1, then f(pi/6) is equal to

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Find the area bounded by the curves y = e^(x), y = |x-1| and x = 2.

    Text Solution

    |

  20. The area bounded by y = 2-|2-x| and y=3/|x| is:

    Text Solution

    |