Home
Class 12
MATHS
Let f(x) = x+ log(e)x-xlog(e)x,x in (0,o...

Let `f(x) = x+ log_(e)x-xlog_(e)x,x in (0,oo)`
List I contains information about zero of f(X) ,f'(x) and f''(x)
List II contains information about the limiting behaviour of f(x), f(x) and f''(x) at infinty
List III contains information about increasing /decreasing nature of f(x) and f'(x)

which o fhte following options is the only CORRECT comibination?

A

III, I, R

B

I, iii ,P

C

II, iii ,P

D

II, IV, Q

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|36 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) =e^(-x) , then f'(x) is ?

If f(x)=log_(a)(log_(a)x) , then f'(x), is

If f(x)=|log_(e) x|,then

If f(x)=log_x(lnx) then f'(x) at x=e is

If f(x)=log_(e)(log_(e)x)/log_(e)x then f'(x) at x = e is

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

If f(x)=sinx+e^x , then f''(x)

Let f(x) = (e^x x cosx-x log_e(1+x)-x)/x^2, x!=0. If f(x) is continuous at x = 0, then f(0) is equal to

If f(x)=log_(x^(2))(logx) ,then f '(x)at x= e is

If f(x)=log_(x) (log x)," then find "f'(x) at x= e

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-JEE Advanced (Archive)
  1. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  2. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  3. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  4. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

  7. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  8. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  9. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  10. The number of distinct real roots of x^(4) - 4x^(3) + 12 x^(2) + x - ...

    Text Solution

    |

  11. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  12. The maximum value of the expression 1/(sin^2theta+3sinthetacostheta+5c...

    Text Solution

    |

  13. The maximum value of the function f(x)=2x^3-15 x^2+36 x-48 on the set ...

    Text Solution

    |

  14. A cylindrical container is to be made from certain solid material with...

    Text Solution

    |

  15. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

  16. Let C be the curve y^(3) - 3xy + 2 =0. If H is the set of points on th...

    Text Solution

    |

  17. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

    Text Solution

    |

  18. if |f(x1)-f(x2)|<=(x1-x2)^2Find the equation of tangent to the curve y...

    Text Solution

    |

  19. The curve y=a x^3+b x^2+c x+5 touches the x-axis at P(-2,0) and cuts t...

    Text Solution

    |

  20. Tangent at a point P(1) [other than (0,0)] on the curve y=x^(3) meets ...

    Text Solution

    |