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

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

Promotional Banner

Topper's Solved these Questions

  • CUET MOCK TEST 2022

    XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

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

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

If x gt -1 , show that : (x)/(sqrt(1+x))-log(1+x)+9 is an increasing function of x.

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

The function log (1+x) - (2x)/(x+2) is increasing in the interval:

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

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

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

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Find the Vector and Cartesian equations of the line passing through...

    Text Solution

    |

  2. Evaluate : int((x-4)e^x)/((x-2)^3)\ dx

    Text Solution

    |

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

    Text Solution

    |

  4. Find the equation of the normal at the point (a m^2, a m^3) for the ...

    Text Solution

    |

  5. Evaluate : int(e^x)/(sqrt(5-4e^x-\ e^(2x)))\ dx

    Text Solution

    |

  6. Find the relationship between a and b so that the function f define...

    Text Solution

    |

  7. If x^y=e^(x-y), show that (dy)/(dx)=(logx)/({log(x e)}^2)

    Text Solution

    |

  8. Obtain the inverse of the following matrix, using elementary operation...

    Text Solution

    |

  9. Using matrices, solve the following system of equations: x+y+z=6; x...

    Text Solution

    |

  10. Find the value of p , if (2 hat i+6 hat j+27 hat k) x ( hat i+3 hat j+...

    Text Solution

    |

  11. Write the direction cosines of a line equally inclined to be three ...

    Text Solution

    |

  12. Let* be a binary operation on N given by a*b = HCF(a ,\ b)\ a ,\ b\...

    Text Solution

    |

  13. Find the value of x, If [[3x+y,-y],[2y-x,3]]=[[1,2],[-5,3]]

    Text Solution

    |

  14. Write the value of the following determinant |(a-b,b-c,c-a),(b-c,c-a,a...

    Text Solution

    |

  15. Find the value of x, from the following: |(x,4),(2,2x)|=0

    Text Solution

    |

  16. Evaluate: int(cossqrt(x))/(sqrt(x))\ dx

    Text Solution

    |

  17. Write the principal value of, cos^(-1)\ (cos(7pi)/6)

    Text Solution

    |

  18. A card from a pack of 52 cards is lost. From the remaining cards of...

    Text Solution

    |

  19. From a lot of 10 bulbs, which includes 3 defectives, a sample of 2 ...

    Text Solution

    |

  20. Solve the following differential equation: (x^3+y^3)dy-x^2y dx=0

    Text Solution

    |