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

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos
  • INDEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|1443 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

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

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

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

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

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

RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
  1. Sol v e(8x^2+16 x-51)/(2x^2+5x-12)>3

    Text Solution

    |

  2. Determine the values of x for which f(x)=x^x , x >0 is increasing or d...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the intervals in which the function f(x)=x^4-(x^3)/3 is increasin...

    Text Solution

    |

  5. Find the intervals in which f(x)=x/(logx) is increasing or decreasing.

    Text Solution

    |

  6. Show that f(x)=cos(2x+pi/4) is an increasing function on (3pi//8,7pi/...

    Text Solution

    |

  7. Show that for a >=1,f(x)=sqrt(3)sinx-cosx-2a x+b is decreasing on Rdot

    Text Solution

    |

  8. Find the values of a for which the function f(x)=(a+2)x^3-3a x^2+9a x-...

    Text Solution

    |

  9. If a , b , c are real numbers, then find the intervals in which f(x)=|...

    Text Solution

    |

  10. Find the intervals in which f(x)=(x-1)^3(x-2)^2 is increasing or decre...

    Text Solution

    |

  11. Find the intervals in which f(x)=(4x^2+1)/x is increasing or decreasin...

    Text Solution

    |

  12. Determine the intervals in which the function f(x)=x^4-8x^3+22 x^2-24 ...

    Text Solution

    |

  13. Find the intervals for which f(x)=x^4-2x^2 increasing or decreasing.

    Text Solution

    |

  14. Determine the values of x for which f(x)=(x-2)/(x+1)x!=-1 is increasin...

    Text Solution

    |

  15. Find the intervals in which f(x)=x/2+2/x , x!=0 is increasing or decre...

    Text Solution

    |

  16. For which values of x , the function f(x)=x/(x^2+1) is increasing and ...

    Text Solution

    |

  17. Find the intervals in which f(x)=(4x^2+1)/x is increasing or decreasi...

    Text Solution

    |

  18. Separate the interval [0,pi/2] into sub intervals in which function f(...

    Text Solution

    |

  19. Show that the function f given by f(x)=tan^(-1)(sinx+cosx), x" ">" "0 ...

    Text Solution

    |

  20. Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3...

    Text Solution

    |