Home
Class 11
MATHS
Show that the function f given by f(x) =...

Show that the function f given by f(x) `= tan^(-1)(sin x + cos x), x gt 0` is always an strictly increasing functions in `(0, (pi)/(4))`

Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise LECTURE SHEET (EXERCISE - I ) (STRAIGHT OBJECTIVE TYPE QUESTIONS)|74 Videos
  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise LECTURE SHEET (EXERCISE - I ) (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS)|8 Videos
  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Exercise - 8.2 (Long Answer Questions)|36 Videos
  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos
  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I (LEVEL-II (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS ) )|2 Videos

Similar Questions

Explore conceptually related problems

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

Show that the function given by f(x) = 7x – 3 is increasing on R.

Show that the function given by f (x) = 3x + 17 is increasing on R.

Prove that the function f given by f(x) = x ^(2) – x + 1 is neither strictly increasing nor decreasing on (– 1, 1).

Show that the function f given by f(x) = x^(3)-3x^(2)+4x,x in R is increasing on R.

Show that the function defined by f(x)= sin (x^2) is a continuous function.

Show that the function defined by f(x)= |cos x| is a continuous function.

Show that the function defined by f(x)= cos (x^2) is a continuous function.

The function f(x) =Tan^(-1) (sin x+ cos x) is an increasing function in

The function f(x)=Tan^(-1) (sinx+cosx) is an increasing function in

AAKASH SERIES-MAXIMA AND MINIMA -Advanced Subjective Type Questions
  1. Show that semi-vertical angle fo right circular cone of given surface ...

    Text Solution

    |

  2. A wire of length 'a' is cut into two parts which are bent in the form ...

    Text Solution

    |

  3. An open top box of maximum possible volume from a square piece of tin ...

    Text Solution

    |

  4. The point on the parabola y =x^(2) + 7x + 2 which is elosest to the li...

    Text Solution

    |

  5. A car starts from a point P at time t = 0 seconds and stops at point Q...

    Text Solution

    |

  6. A water tank has the shape of an inverted right circular cone with its...

    Text Solution

    |

  7. A tank with rectangular base and rectangular side, open at the top is ...

    Text Solution

    |

  8. If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x ...

    Text Solution

    |

  9. If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x ...

    Text Solution

    |

  10. If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x ...

    Text Solution

    |

  11. Let f(x) = {(" "x e^(a x), x le 0),(x + a x^(2) - x^(3) , x ...

    Text Solution

    |

  12. Find the intervals in which f(x) = int(0)^(x){e^(t) - 1)(t+1)(t-2)(t+4...

    Text Solution

    |

  13. A point on the hypotenuse of a triangle is at distance a and b from th...

    Text Solution

    |

  14. Let f, g, h be real valued functions defined on the interval [0, 1] by...

    Text Solution

    |

  15. Find the equation of tangents to the curve y = cos(x+y), -2pi le x le ...

    Text Solution

    |

  16. If f(x) = int(x)^(x^(2)) (t-1)dt, 1 le x le 2, find the greatest value...

    Text Solution

    |

  17. Find intervals in which the function given by f(x) = (3)/(10)x^(4) - (...

    Text Solution

    |

  18. Show that the function f given by f(x) = tan^(-1)(sin x + cos x), x gt...

    Text Solution

    |

  19. Show that t height of the cylinder of greatest volume which can be ins...

    Text Solution

    |

  20. Let f(x) = (1+b^(2))x^(2) + 2bx + 1 and let m (b) be the minimum value...

    Text Solution

    |