Home
Class 12
MATHS
Show that y=log(1+x)-(2x)/(2+x), x >-1, ...

Show that `y=log(1+x)-(2x)/(2+x), x >-1`, is an increasing function of x throughout its domain.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.3|31 Videos

  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.4|23 Videos

  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.1|18 Videos

  • APPLICATION OF INTEGRALS

    NCERT GUJARATI|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Show that y=log(1+x)-(2x)/(2+x), x gt -1 , is an increasing function of x throughout its domain.

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

Show that the function given by f(x)=e^(2x) is increasing on R.

f(x)=log(x-[x]) , where [*] denotes the greatest integer function. find the domain of f(x).

Integrate the function in Exercise. x log 2x

If f(x)=(x^(2)-x)/(x^(2)+2x) , then find the domain and range of f. Show that f is one-one. Also, find the function (d(f^(-1)(x)))/(dx) and its domain.

A variable y increases from y_(1)=2 to y_(2)=8 linearly with another variable x in the interval x_(1)=0 to x_(2)=10 . Express y as function of x and draw its graph.

x log x(dy)/(dx) + y = (2)/(x)log x

f(x)=sqrt((log(x-1))/(x^(2)-2x-8)) . Find the domain of f(x).

Range of f(x)=[1/(log(x^(2)+e))]+1/sqrt(1+x^(2)), where [*] denotes greatest integer function, is

NCERT GUJARATI-APPLICATION OF DERIVATIVES-EXERCISE 6.2
  1. Find the intervals in which the function f given by f(x)=2x^2-3xis(a) ...

    Text Solution

    |

  2. Find the intervals in which the function f given by f(x)=2x^3-3x^2-36 ...

    Text Solution

    |

  3. Find the intervals in which the following functions are strictly in...

    Text Solution

    |

  4. Find the interval in which the following function are strictly increas...

    Text Solution

    |

  5. Find the intervals in which the given functions are strictly increasin...

    Text Solution

    |

  6. Find the intervals in which the functions are strictly increasing or ...

    Text Solution

    |

  7. Find the intervals in which the functions are strictly increasing or ...

    Text Solution

    |

  8. Show that y=log(1+x)-(2x)/(2+x), x >-1, is an increasing function of x...

    Text Solution

    |

  9. Find the values of x for which y=[x(x-2)]^2is an increasing function

    Text Solution

    |

  10. Prove that y=(4sintheta)/((2+costheta)-theta is an increasing function...

    Text Solution

    |

  11. Prove that the logarithmic function is strictly increasing on (0,oo).

    Text Solution

    |

  12. Prove that the function f given by f(x) = x ^(2) – x + 1 is neither st...

    Text Solution

    |

  13. Which of the following functions is not decreasing on (0,pi//2)?

    Text Solution

    |

  14. On which of the following intervals is the function f given by f(x) = ...

    Text Solution

    |

  15. Find the least value of a such that the function f given by f(x)=x^2+...

    Text Solution

    |

  16. Let P be an interior point of triangle ABC. Let Q and R be the reflec...

    Text Solution

    |

  17. Prove that the function f given by f" "(x)" "=" "log" "cos" "x is stri...

    Text Solution

    |

  18. Prove that the function f given by f (x) = log |cos x| is decreasing o...

    Text Solution

    |

  19. Prove that the function given by f(x)=x^3-3x^2+3x-100is increasing in...

    Text Solution

    |

  20. The interval in which y=x^2""e^(-x) is increasing is (A) (-oo,""""o...

    Text Solution

    |