Home
Class 12
MATHS
Let f:(0,oo)->R be a differentiable func...

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

A

`lim_(xto0+)int'((1)/(x))=1`

B

`lim_(xto0+)x int'((1)/(x))=1`

C

`lim_(xto0+)x^(2)'((1)/(x))=1`

D

`|f(x)|le2` for all `x in(0,2)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|4 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

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

If f:R rarr R is a differentiable function such that f(x)>2f(x) for all x in R and f(0)=1, then

if f:R rarr R is a differentiable function such that f'(x)>2f(x) for all x varepsilon R, and f(0)=1, then

Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int_(1)^(x)f(t)dt=3xf(x)-x^(3) for all x>=1, then the value of f(2) is

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let f:[0,oo)rarr R be a function satisfying f(x)e^(f(x))=x, for all x in[0,oo). Prove taht

ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f:R-{-1}toR and f is differentiable function satisfies: f((x)+f(y...

    Text Solution

    |

  2. A solution curve of the differential equation (x^2+xy+4x+2y+4)((dy)/(d...

    Text Solution

    |

  3. Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x ...

    Text Solution

    |

  4. Let y(x) be a solution of the differential equation (1+e^x)y^(prime...

    Text Solution

    |

  5. Consider the family of all circles whose centers lie on the straigh...

    Text Solution

    |

  6. The function y=f(x) is the solution of the differential equation [dy]/...

    Text Solution

    |

  7. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  8. A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...

    Text Solution

    |

  9. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  10. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  11. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  12. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

    Text Solution

    |

  13. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

    Text Solution

    |

  14. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  15. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

    Text Solution

    |

  16. For the following question, choose the correct answer from the codes (...

    Text Solution

    |

  17. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

    Text Solution

    |

  18. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

    Text Solution

    |

  19. Let the population of rabbits surviving at a time t be governed by ...

    Text Solution

    |

  20. At present a firm is manufacturing 2000 items. It is estimated that th...

    Text Solution

    |