Home
Class 12
MATHS
Use the function f(x)=x^(1//x),xgt0 to d...

Use the function `f(x)=x^(1//x),xgt0` to determine the bigger of the two numbers `e^pi` and `pi^e`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

Use the function f(x)=x^(1/x), x gt 0 , to determine the bigger of the two numbers e^(pi) and pi^(e) .

Integrate the functions 1/(x(logx)^(m)),xgt0,mne1

Show that the function f(x)=(x+2)/(x+1)(xgt0) decreasing.

The function f(x)=(ln(pi+x))/(ln(e+x)) is

Consider the functions f_(1)(x)=x,f_(2)(x)=2+log_(e )x, x gt 0 . The graphs of the functions intersect

Let exp(x) denote exponential function e^x . If f(x)=exp(x^(1/x)).xgt0 then the minimum value of f in the interval [2,5] is

Find the number of points where the function f(x) = max(|tanx|,cos|x|) is non-differentiable in the interval (-pi,pi) .

Find the range of the function f(x) = (e^x - e^-x) .

If f f(x)=mux-sinx, xgt0 is a monotonic increasing function then -

The function f(x) =(1-sinx)/((pi-2x)^(2)) is underfined at x=(pi)/(2) .Redefine the function f(x) so as to make it continuous at x=(pi)/(2) .

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. The number of critical points of f(x)=(|x-1|)/X^2 is

    Text Solution

    |

  2. The function f(x)=oversetxunderset(-1)intt(e^t-1)(t-1)(t-2)^3(t-3)^5 d...

    Text Solution

    |

  3. Use the function f(x)=x^(1//x),xgt0 to determine the bigger of the two...

    Text Solution

    |

  4. Show that (x^5-5x^4+5x^3-1) has a local maximum when x = 1, a local mi...

    Text Solution

    |

  5. Find the point on the parabola y^2=2x which is closest to the point (1...

    Text Solution

    |

  6. In a right -angled triangle, prove that r+2R=S.

    Text Solution

    |

  7. Show that the semivertical angle of a cone of maximum volume and of gi...

    Text Solution

    |

  8. Let f(x)={(|x-2|+a^2-9a-9,ifxlt2, 2x-3 ,ifxge2:} Then find value of 'a...

    Text Solution

    |

  9. Find the values of 'm' for which the equation x^4-(m-3)x^2+m=0 has Fo...

    Text Solution

    |

  10. The difference between the greatest and least values of the function f...

    Text Solution

    |

  11. The tangent and normal to the curve y=2sinx+sin2x are drown at P(x=pi/...

    Text Solution

    |

  12. Show that the sum of the intercepts of the tangent to the curve sqrtx+...

    Text Solution

    |

  13. Find the point on the curve y-e^(xy)+x=0. At which we have vertical ta...

    Text Solution

    |

  14. Find the lengths of tangent, subtangent, normal and subnormal to y^2=4...

    Text Solution

    |

  15. If the length of subnormal is equal to length of subtangent at a point...

    Text Solution

    |

  16. Find the angle of intersection between the following curves, y^2=4x an...

    Text Solution

    |

  17. Show that x=y^2 and xy = k cut orthogonally if 8k^2=1

    Text Solution

    |

  18. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

    Text Solution

    |

  19. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

    Text Solution

    |

  20. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

    Text Solution

    |