Home
Class 12
MATHS
Let f(x) be a non-positive continuous fu...

Let `f(x)` be a non-positive continuous function and `F(x)=int_(0)^(x)f(t)dt AA x ge0` and `f(x) ge cF(x)` where `c lt 0` and let `g:[0, infty) to R` be a function such that `(dg(x))/(dx) lt g(x) AA x gt 0` and `g(0)=0`
The solution set of inequation `g(x)(cos^(-1)x-sin^(-1)) le0`

A

`[-1,1/sqrt(2)]`

B

`[1/sqrt(2),1]`

C

`[0,1/sqrt(2)]`

D

`[0,1/sqrt(2)]`

Text Solution

Verified by Experts

The correct Answer is:
A
`g(x) (cos^(-1)x-sin^(-1)x) le0`
or `(cos^(-1)x-sin^(-1)x) ge0` or `x in [-1, 1/sqrt(2)]`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Let f(x), xge0 , be a non-negative continous function,and let F(x) = int_(0)^(x)f(t)dt, xge0 , if for some cgt0,f(x)lec F(x) for all xge0 , then show that f(x)=0 for all xge0 .

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f be an odd continous function which is periodic with priod 2 if g(x) = int_0^x f(t) dt then

The points of extrema of the function f(x)= int_(0)^(x)(sin t)/(t)dt in the domain x gt 0 are-

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1) =1 , then

f(x)=e^x.g(x) , g(0)=2 and g'(0)=1 then f'(0)=

Let g(x) = int_(x)^(2x) f(t) dt where x gt 0 and f be continuous function and 2* f(2x)=f(x) , then

let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in[0,a] then int_0^a dx/(1+e^f(x) is equal to

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b If f(x) is an odd function, then

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b If f(x) is an even function, then

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  2. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  3. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  4. A curve C with negative slope through the point (0, 1) lies in the fir...

    Text Solution

    |

  5. A curve 'C' with negative slope through the point(0,1) lies in the I Q...

    Text Solution

    |

  6. A curve C with negative slope through the point (0, 1) lies in the fir...

    Text Solution

    |

  7. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int(0)...

    Text Solution

    |

  8. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int(0...

    Text Solution

    |

  9. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int(0...

    Text Solution

    |

  10. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  11. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  12. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  13. Consider a tank which initially holds V(0) liter of brine that contain...

    Text Solution

    |

  14. A 50 L tank initailly contains 10 L of fresh water, At t=0, a brine so...

    Text Solution

    |

  15. In the above question, the amount of salt in the tank at the moment of...

    Text Solution

    |

  16. Match the following lists:

    Text Solution

    |

  17. Match the following lists:

    Text Solution

    |

  18. Match the differential equation in List I with its solution in List II...

    Text Solution

    |

  19. If y=y(x) and it follows the relation 4x e^(x y)=y+5sin^2x , then ...

    Text Solution

    |

  20. If x(dy)/(x t)=x^2+y-2,y(1)=1, then y(2) equal

    Text Solution

    |