Home
Class 12
MATHS
Show that f(x) = 2x+cot^(-1)x+ log(sqrt(...

Show that `f(x) = 2x+cot^(-1)x+ log(sqrt(1+x^(2))-x)` is increasing in R.

A

increases on R

B

decreases in `[0,oo)`

C

neither increasing nor decreasing in `(0,oo)`

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

Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) is increasing on R .

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

Show that f(x)=e^(2x) is increasing on R .

Show that f(x) =(x)/(sqrt(1+x)) =en (1+x) is an increasing function for x gt-1

If f(x) = (tan^-1 x)^2+2/(sqrt(x^2+1) then f is increasing in

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)

The function f(x)=log (1+x)-(2+x) is increasing in

Let f(x)=2x-tan^-1 x- ln(x+sqrt(1+x^2)); x in R, then

The function f(x) = sec[log(x + sqrt(1+x^2))] is

The function f(x) = sec[log(x + sqrt(1+x^2))] is

OBJECTIVE RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTIONS-Exercise
  1. Which of the following functions is not decreasing on (0,pi//2)?

    Text Solution

    |

  2. Let f'(x)=f(x)(x-a)^(2), where g(a) ne 0 and g is continuous at x=a t...

    Text Solution

    |

  3. Show that f(x) = 2x+cot^(-1)x+ log(sqrt(1+x^(2))-x) is increasing in R...

    Text Solution

    |

  4. The function f(x)=log (1+x)-(2+x) is increasing in

    Text Solution

    |

  5. On which of the following intervals in the function f(x)=2x^2-log|x|,x...

    Text Solution

    |

  6. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

    Text Solution

    |

  7. The function f(x)=(asinx+b cosx)/(c sinx+d cos x) is decreasing, if

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |