Home
Class 12
MATHS
If d is the minimum distance between th...

If `d` is the minimum distance between the curves `f(x)=e^x a n dg(x)=(log)_e x ,` then the value of `d^6` is

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

If f(x)=log_(x)(log_(e)x) , then the value of f'(e ) is -

IF f(x)= log_x(logx) then the value of f'(e) is

The area bounded by the curves y=(log)_e xa n dy=((log)_e x)^2 is

If f(x)=e^x and g(x) =log_(e)x, then find (f+g)(1) and fg(1).

If f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x))+2 , then the value of f^(-1)(x) is -

Find the cosine of the angle of intersection of curves f(x)=2^x(log)_e xa n dg(x)=x^(2x)-1.

Plot the curve y=(log)_e(-x)dot

If f (x) =(e^(x) -e ^(-x))/( e ^(x) +e^(-x)) +2, then the value of f ^(-1) (x) is-

If f(x)=log_5log_3 x , then f'(e ) is equal to

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Find the equation of tangent and normal to the curve x=(2a t^2)/((1+t^...

    Text Solution

    |

  2. Find the points on the curve 5x^2-8x y+5y^2=4 whose distance from the ...

    Text Solution

    |

  3. If d is the minimum distance between the curves f(x)=e^x a n dg(x)=(l...

    Text Solution

    |

  4. L L ' is the latus rectum of the parabola y^2= 4ax and PP' is a doubl...

    Text Solution

    |

  5. Let f(x0 be a non-constant thrice differentiable function defined on (...

    Text Solution

    |

  6. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

    Text Solution

    |

  7. Points on the curve f(x)=x/(1-x^2) where the tangent is inclined at an...

    Text Solution

    |

  8. The sum of the perimeter of a circle and square is k, where k is so...

    Text Solution

    |

  9. Separate the intervals of monotonocity for the function f(x)=x^2e^(-x)

    Text Solution

    |

  10. If f is a continuous function on [0,1], differentiable in (0, 1) such ...

    Text Solution

    |

  11. Separate the intervals of monotonocity for the function f(x)=-2x^3-9x^...

    Text Solution

    |

  12. Given g(x)=(x+2)/(x-1) and the line 3x+y-10=0. Then the line is tangen...

    Text Solution

    |

  13. Let g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot Then prov...

    Text Solution

    |

  14. Let f be a continuous, differentiable, and bijective function. If the ...

    Text Solution

    |

  15. Find the intervals of decrease and increase for the function f(x)=cos(...

    Text Solution

    |

  16. If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that ...

    Text Solution

    |

  17. Find the interval of monotonocity of the function f(x)=|x-1|/x^2dot

    Text Solution

    |

  18. A continuous and differentiable function y=f(x) is such that its graph...

    Text Solution

    |

  19. Find the intervals in which the function f given by f(x)=(4sinx-2x-xc...

    Text Solution

    |

  20. If f(x) is continuous in [a , b] and differentiable in (a,b), then pro...

    Text Solution

    |