Home
Class 12
MATHS
Column I, Column II int(e^(2x)-1)/(e^...

Column I, Column II `int(e^(2x)-1)/(e^(2x)+1)dxi se q u a lto` , p. `x-log""[1+sqrt(1-e^(2x))]+c` `int1/((e^x+e^(-x))^2)dxi se q u a lto` , q. `log(e^x+1)-x-e^(-x)+c` `int(e^(-x))/(1+e^x)dxi se q u a lto` , r. `log(e^(2x)+1)-x+c` `int1/(sqrt(1-e^(2x)))dxi se q u a lto` , s. `-1/(2(e^(2x)+1))+c`

A

an increasing function R

B

a decreasing function on R

C

an even function on R

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos

  • HEIGHTS AND DISTANCES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|45 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

intsin^(-1)((2x)/(1+x^2))dx is e q u a lto

int(e^x)/((1+e^x)(2+e^x))dx

If y=intsqrt(x)(1+x^(1/3))^4dx"i se q u a lto"

int_(0)^(1)e^(2x)e^(e^(x) dx =)

Evaluate: int(e^(2x))/(1+e^x)dx

Evaluate: int(e^x)/(1+e^(2x))dx

Evaluate: int(e^x)/(1+e^(2x))dx

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

int_- 1^1(e^(-1/ x))/(x^2(1+e^(-2/ x)))dx is equal to :

OBJECTIVE RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTIONS-Exercise
  1. The function f(x)=(asinx+b cosx)/(c sinx+d cos x) is decreasing, if

    Text Solution

    |

  2. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then k<3 (b) ...

    Text Solution

    |

  3. Find the value of a for which the function (a+2)x^3-3a x^2+9a x-1 decr...

    Text Solution

    |

  4. The function y=x^3-3x^2+6x-17

    Text Solution

    |

  5. The interval in which the function x^3 increases less rapidly than 6x...

    Text Solution

    |

  6. The interval in which the function f(x)=sin x-cos x -ax +b decreases f...

    Text Solution

    |

  7. The function y=cot^(-1) x- log (x+sqrt(x^2+1)) is decreasing in

    Text Solution

    |

  8. the function(|x-1|)/(x^(2)) is monotonically decreasing at the point

    Text Solution

    |

  9. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

    Text Solution

    |

  10. A function is matched below against an interval where it is supposed t...

    Text Solution

    |

  11. A condition for a function y=f(x) to have an inverse is that it should...

    Text Solution

    |

  12. Let g(x)=f(x)+f(1-x) and f''(x)<0, when x in (0,1). Then f(x) is

    Text Solution

    |

  13. The function f(x)=(ln(pi+x))/(ln(e+x)) is

    Text Solution

    |

  14. Column I, Column II int(e^(2x)-1)/(e^(2x)+1)dxi se q u a lto , p. x...

    Text Solution

    |

  15. y={x(x-3)^2 increases for all values of x lying in the interval

    Text Solution

    |

  16. If a lt 0 and f(x)=e^(ax )+ e^(-ax) is monotonically decreasing . F...

    Text Solution

    |

  17. The function f(x) = tanx - x

    Text Solution

    |

  18. The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) ...

    Text Solution

    |

  19. The function f(x)=(log)e(x^3+sqrt(x^6+1)) is of the following types: (...

    Text Solution

    |

  20. Let f(x)=x^3-6x^2+15 x+3 . Then, (a) f(x)>0 for all x in R (b) f(x)>...

    Text Solution

    |