Home
Class 12
MATHS
If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) ...

If `f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x)` then `f(x)` increase in `(0,oo)` decrease in `[0,oo]` neither increases nor decreases in `[0,oo]` increase in `(-oo,oo)`

A

Decreases on `(-oo,oo)`

B

Decreases on `[0,oo)`

C

Neither decreases nor increases on `[0,oo)`

D

Increases on `(-oo,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|36 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Level -1|102 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is (a). increasing in (0,3a) decreasing in (3a, 4a) (b). increasing in (a, 4a) decreasing in (5a ,oo) (c). increasing in (0,4a) (d). none of these

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

Let f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1), then: (a) g is increasing on (1,oo) (b) g is decreasing on (1,oo) (c) g is increasing on (1,2) and decreasing on (2,oo) (d) g is decreasing on (1,2) and increasing on (2,oo)

Show that f(x)=1/(1+x^2) decreases in the interval [0,oo) and increases in the interval (-oo,0]dot

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then (a) f(x) is an increasing function in (0,oo) (b) f(x) is a decreasing function in (-oo,oo) (c) f(x) is an increasing function in (-oo,oo) (d) f(x) is a decreasing function in (-oo,0)

Show that f(x)=1/(1+x^2) decreases in the interval [0,\ oo) and increases in the interval (-oo,\ 0] .

If f(x)=(|x-1)/(x^2) the f(x) is one-one in (2,oo) b. one-one in (0,1) c. one-one in (-oo,0) d. one-one in (1,2)

log(1+x+x^(2)+...oo)=

If f(x) = 1//x, g(x) = sqrt(x) for all x in (0,oo) , then find (gof)(x).

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-Level -2
  1. f(x)=int0^x(e^t-1)(t-1)(sint-cost)sin t dt ,AAx in (-pi/2, 2pi), the...

    Text Solution

    |

  2. l1 and l2 are the side lengths of two variable squares S1, and S2, re...

    Text Solution

    |

  3. If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) increase in (0,oo) ...

    Text Solution

    |

  4. Let f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...

    Text Solution

    |

  5. If are positive integers, maximum value of x^(m) (a-x)^(n)" in (0,a)...

    Text Solution

    |

  6. The maximum value of (sin x)^((sin x)) is

    Text Solution

    |

  7. A helicopter flying along the path y=7+x^((3)/(2)), A soldier standint...

    Text Solution

    |

  8. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

    Text Solution

    |

  9. The largest term in the sequence an=(n^2)/(n^3+200) is given by (529)/...

    Text Solution

    |

  10. The least value of f (x) =x^3/3-abx occurs at x=

    Text Solution

    |

  11. For the curve defined as y=cosec^(-1)((1+x^2)/(2x))+sec^(-1)((1+x^2)/(...

    Text Solution

    |

  12. If f(x)=max{x^(2)-4,|x-2|,|x-4|} then:

    Text Solution

    |

  13. Given that f (x) is a non-constant linear function. Then the curves :

    Text Solution

    |

  14. If a curve with equation of the form y=ax^(4)+bx^(3)+cx+d has zero gra...

    Text Solution

    |

  15. If the area of the triangle included between the axes and any tangent ...

    Text Solution

    |

  16. Show that the maximum value of (1/x)^x is e^(1//e) .

    Text Solution

    |

  17. Consider, f (x) is a function such that f(1)=1, f(2)=4 and f(3)=9 ...

    Text Solution

    |

  18. Statement 1 : f(x)=log(e+x) (pi+x) is strictly increasing for all . ...

    Text Solution

    |

  19. The largest area of the trapezium inscribed in a semi-circle or radius...

    Text Solution

    |

  20. The points of extremum of phi (x)=int(1)^(x)e^(-t^(2//2)) (1-t^(2)) dt...

    Text Solution

    |