Home
Class 12
MATHS
Let f(x) =x - tan^(-1)x. Prove that f(x)...

Let f(x) =x - `tan^(-1)x.` Prove that f(x) is monotonically increasing for `x in R`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise -1A|5 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise -1B|6 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise High Level Problems (HLP)|35 Videos
  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = tan^-1 (g(x)) , where g (x) is monotonically increasing for 0 < x < pi/2.

Let f(x) =e^(2x) -ae^(x)+1. Prove that f(x) cannot be monotonically decreasing for AA x in R for any value of a

Find possible values of 'a' such that f(x) =e^(2x) -2(a^(2) -21) e^(x)+ 8x+5 is monotonically increasing for x in R.

Let set of all possible values of lamda such that f (x)= e ^(2x) - (lamda+1) e ^(x) +2x is monotonically increasing for AA x in R is (-oo, k]. Find the value of k.

Prove that f (x) = e^(3x) is strictly increasing function on R.

f(x)=2x-tan^(-1)x-log{x+sqrt(x^2+1)} is monotonically increasing when (a) x >0 (b) x<0 (c) x in R (d) x in R-{0}

f(x)=[x] is step-up function. Is it a monotonically increasing function for x in R ?

Find the possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is monotonically increasing for x in Rdot

Find the possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is monotonically increasing for x in Rdot

Let f(x) be and even function in R. If f(x) is monotonically increasing in [2, 6], then

RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-Self Practice Problems
  1. A hot air balloon rising straight up from a level field is tracked by ...

    Text Solution

    |

  2. Find the intervals of monotonicity of the following functions. (i...

    Text Solution

    |

  3. Let f(x) =x - tan^(-1)x. Prove that f(x) is monotonically increasing ...

    Text Solution

    |

  4. Find the range of values of a if f(x)=2e^x-a e^(-x)+(2a+1)x-3 is monot...

    Text Solution

    |

  5. Let f(x) =e^(2x) -ae^(x)+1.Prove that f(x) cannot be monotonically d...

    Text Solution

    |

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

    Text Solution

    |

  7. For each of the following graph comment on monotonically of f(x) ...

    Text Solution

    |

  8. Let f(x)=x^3-3x^2+ 3x + 4, comment on the monotonic behaviour of f(x) ...

    Text Solution

    |

  9. Draw the graph of function f(x)={underset([x] " "1 le x le 2)(x " ...

    Text Solution

    |

  10. In each of following graphs identify if x= a is point of local maxi...

    Text Solution

    |

  11. Examine the graph of following functions in each case identify the p...

    Text Solution

    |

  12. Find the points of local maxima or minima of following functions...

    Text Solution

    |

  13. Let f(x) =x^(3) -x^(2) -x-4 (i) find the possible points of maxim...

    Text Solution

    |

  14. Let f(x) =x +(1)/(x). find local maximum and local minimum value ...

    Text Solution

    |

  15. if f(x) ={underset( cos x " "x ge 0)((x+lambda)^(2) " " x lt 0). ...

    Text Solution

    |

  16. Let f(x) = sin x (1+cos x) , x in (0,2pi). Find the number of criti...

    Text Solution

    |

  17. Find the two positive numbers x and y whose sum is 35 and the ...

    Text Solution

    |

  18. A square piece of tin of side 18 cm is to be made into a box withou...

    Text Solution

    |

  19. A square piece of tin of side 18 cm is to be made into a box w...

    Text Solution

    |

  20. The maximum distance of the centre of the ellipse x^2/(81)+y^2/(25)=1 ...

    Text Solution

    |