Home
Class 12
MATHS
Show that ,the maximum value of ((1)/(x...

Show that ,the maximum value of `((1)/(x))^(x)` is `e^((1)/(e)`

A

`e^(e )`

B

`e^(-e)`

C

`-e^(e )`

D

`e^(1//2)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MATHEMATICS (2011)

    WB JEE PREVIOUS YEAR PAPER|Exercise DESCRIPTIVE TYPE QUESTIONS|10 Videos

  • QUESTION PAPER 2008

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|80 Videos

Similar Questions

Explore conceptually related problems

Using calculus, show that the maximum value of the function (1/x)^x is e^(1/e) .

Prove that The maximum value of (sqrt(-3+4x-x^2)+4)^2+(x-5)^2(w h e r e1lt=xlt=3) i s 36.

The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 (d) 0

The maximum value of x^4e^ (-x^2) is (A) e^2 (B) e^(-2) (C) 12 e^(-2) (D) 4e^(-2)

The value of int e^(-(1)/(x)) cdot (1)/(x^(2)) dx is-

Find the value of (d)/(dx)(x(e^(x)+e^(4x))/(e^(x)+e^(-2x))) .

If f(x)=int_(1)^(x)(log_(e)t)/(1+t)dt , where xgt0 , find the value of f(x)+f((1)/(x)) and hence show that, f(e)+f((1)/(e))=(1)/(2) .

The value of int (e^(tan^(-1)x)dx)/(1+x^(2)) is -

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d)

Show that, underset(x to 0) lim ((x-1+cosx)/(x))^(1/x)=(1)/(sqrt(e ))

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2007-MULTIPLE CHOICE QUESTIONS
  1. Let f(x)=a^(x)(a gt 0) be written as f(x)=g(x)+h(x), when g (x) is an ...

    Text Solution

    |

  2. A=[(-i,0),(0,i)] then A^(T)A= (where I is 2xx2 identity matrix)

    Text Solution

    |

  3. Show that ,the maximum value of ((1)/(x))^(x) is e^((1)/(e)

    Text Solution

    |

  4. The value of the integeral int(-pi//7)^(pi//7)x^(3) cos^(2)x dx is

    Text Solution

    |

  5. The sum of the series 1+(1)/(3.9)+(1)/(5.81)+(1)/(7.729)+……. to oo is

    Text Solution

    |

  6. Using integration find the area of the region bounded by the parabola ...

    Text Solution

    |

  7. If m and n denote respectively the order and degree of a differential ...

    Text Solution

    |

  8. A particle is moving along the x - axis in such a way that it has disp...

    Text Solution

    |

  9. The identity mapping I(c ) : S to S is defined as I(s)(x)=x for x in S...

    Text Solution

    |

  10. If z = x + iy and arg ((z-1)/(z+1))=(pi)/(4), then the locus of (x, y)...

    Text Solution

    |

  11. Solve the equation (dy)/(dx)+y/x=x^2

    Text Solution

    |

  12. A partiole is moving in a straight line such that its velocity at time...

    Text Solution

    |

  13. For an integrable function f (x) in [-3, 3], which of the following is...

    Text Solution

    |

  14. The area bounded by the parabola y^(2)=2x+1 and the line x-y=1 is

    Text Solution

    |

  15. If the circles x^(2)+y^(2)-4r x-2ry+4r^(2)=0 and x^(2)+y^(2)=25 touch ...

    Text Solution

    |

  16. The minimum value of 6 cos alpha + 8 sin alpha + 11 is

    Text Solution

    |

  17. If alpha, beta be the roots of the equation x^(2)+x+1=0, the value of ...

    Text Solution

    |

  18. If A=[(0,3),(4,5)] and kA=[(0,4a),(3b,60)], then the values of k, a an...

    Text Solution

    |

  19. Let f(x)=(ax)/(x+1), x ne1, then the value of 'a' for which f[f(x)]=x ...

    Text Solution

    |

  20. If x in[0,6], the probability that the expression x^(2)-7x+10 ge 0 is

    Text Solution

    |