Home
Class 12
MATHS
If x> - 1 , show that x/(sqrt(1+x))-log(...

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

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE|433 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise EXERCISE|211 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 the function f (x) = (x)/(1+|x|) is a strict increasing function.

Show that y = log (1 + x) - (2x)/(2 + x) is strictly increasing funtion of x for all values of x gt - 1 .

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

Show that the function f(x) = x -(1)/(x) is a strict increasing function fox x > 0

Show that the function x+1/x, x ge 1 is increasing.

Show that the function x^2 - x+1 is neither increasing nor decreasing on (0,1).

Show that the function f(x)=x^(7)+8x^(5)+1 is increasing function for all values of x.

If x^y = e^(x + y) , show that (dy)/(dx) = (log x - 2)/((1 - log x)^2)

MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Which of the following functions are strictly decreasing on ( 0, pi/2 ...

    Text Solution

    |

  2. If y = 4x-(x^2)/(2), when 'x' denotes the number of hours worked and y...

    Text Solution

    |

  3. If x> - 1 , show that x/(sqrt(1+x))-log(1+x) + 9 is an increasing func...

    Text Solution

    |

  4. Find the slopes of the tangents to the following curves: y=3x^2 at x =...

    Text Solution

    |

  5. Find the slope of the tangent to the curve y = x^3-x at x=2

    Text Solution

    |

  6. Find the slope of the tangent to the curve y = 3x^4 - 4x at x = 4 .

    Text Solution

    |

  7. Find the slope of the tangent to the curve y = 3x^4 - 4x at x = 4 .

    Text Solution

    |

  8. Find the slope of the tangent to the curve y = (x-1)/(x-2) at x = 10.

    Text Solution

    |

  9. Find the slope of the tangent to the curve y = x^3-3x+2 at the point w...

    Text Solution

    |

  10. Find the slope of the tangent to the curve y = x^3-x^2+1 at the point ...

    Text Solution

    |

  11. Find the slope of the tangent to the curve: y = 3x^2 - 6x at the point...

    Text Solution

    |

  12. Find the slope of the tangent to the curve: y=x^3 - 2x+8 at the point ...

    Text Solution

    |

  13. Find the slope of the normal to the curve: y=2x^2 - 1 at (1,1)

    Text Solution

    |

  14. Find the slope of the tangent to the curve y = x^3-x^2+1 at the point ...

    Text Solution

    |

  15. Find the slope of the tangent to the curve: y = tan^2x+sec x at x = pi...

    Text Solution

    |

  16. Find the slope of the tangent to the curve: x = a(theta-sintheta), y =...

    Text Solution

    |

  17. Find the slope of the tangent to the curve: x = 1-a sintheta, y = b co...

    Text Solution

    |

  18. Find the slope of the tangent to the curve: x=acos^3theta, y = asin^3 ...

    Text Solution

    |

  19. Find the equations of the tangent line to the curve: y = 2x^2 + 3y^2 =...

    Text Solution

    |

  20. Find the equations of the tangent line to the curve: y=x^3 - 3x +5 at ...

    Text Solution

    |