Home
Class 12
MATHS
Minunun distance between the curves f(x)...

Minunun distance between the curves `f(x)=e^x and g(x)=ln x` is

A

1

B

`sqrt(2)`

C

2

D

e

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part II|21 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part III|23 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise 1 Part III : Match the Column|4 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

If d is the minimum distance between the curves f(x)=e^(x) and (x)=(log)_(e)x, then the value of d^(6) is

The area between the curves y=ln x and y=(ln x)^(2) is

The minimum distance between a point on the curve y=e^(x) and a point on the curve y=log_(e)x is

The minimum distance between a point on the curve y=e^(x) and a point on the curve y=log_(e)x is -

Find the shortest distance between the curves f(x)=-6x^(6)-3x^(4)-4x^(2)-6 and g(x)=e^(x)+e^(-x)+2

Given f(x) = int_(0)^(x)e^(t)(ln sec t - sec ^(2) t ) dt, g(x)= - 2e^(x) tan x Find the area bounded by the curves y = f(x) and y = g(x) between the ordinates x = 0 and x = pi/3

Find the cosine of the angle of intersection of curves f(x)=2^(x)log_(e)x and g(x)=x^(2x)-1

RESONANCE-APPLICATION OF DERIVATIVES-Exersise-2 Part I
  1. Q. Number of tangents drawn from the point (-1/2, 0) to the curve y=e^...

    Text Solution

    |

  2. "Let "f(x) ={ underset( x^(2) +8 " "." "x ge0)(-x^(2)" "." "x lt0)...

    Text Solution

    |

  3. Minunun distance between the curves f(x)=e^x and g(x)=ln x is

    Text Solution

    |

  4. The point(s) on the parabola y^2 = 4x which are closest to the circlex...

    Text Solution

    |

  5. If f(x)= a^({a^(|x|)sgn x }),g(x)=a^([a^(|x|)sgn x] for a gt 1, a!=1...

    Text Solution

    |

  6. If f:[1,10]->[1,10] is a non-decreasing function and g:[1,10]->[1,10] ...

    Text Solution

    |

  7. If f(x)=|ax-b|+c|x| is stricly increasing at atleast one point of non ...

    Text Solution

    |

  8. If g(x) is a curve which is obtained by the reflection of f(x) = (e^x...

    Text Solution

    |

  9. The set of values of p for which the points of extremum of the functio...

    Text Solution

    |

  10. The values of parameter a for which the point of minimum of the functi...

    Text Solution

    |

  11. Consider the following statements : S(1): The function y=(2x^(2)-1)...

    Text Solution

    |

  12. Q. Let f (x)=sin^3x+ lambdasin^2x where (pi)/2 ltxlt (pi)/2. The inte...

    Text Solution

    |

  13. "Let "f(x) ={underset(-2x + log(2) (b^(2)-2), x gt1)(x^(3) -x^(2) +10 ...

    Text Solution

    |

  14. Four points A, B, C, D lie in that order on the parabola y = ax^2 +bx+...

    Text Solution

    |

  15. The base of prism is equilateral triangle. The distance from the centr...

    Text Solution

    |

  16. The maximum area of the rectangle whose sides pass through the vertice...

    Text Solution

    |

  17. Statement 1: ABC is given triangle having respective sides a,b,c. D,E,...

    Text Solution

    |

  18. if f'(x)=(x -4) (x-5) (x-6) (x-7) then.

    Text Solution

    |

  19. Show that the square roots of two successive natural numbers greater ...

    Text Solution

    |

  20. If Rolle's theorems applicable to the function f(x)=ln x/x, (x> 0) ove...

    Text Solution

    |