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

  • 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

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) .

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The function y=2x^2-log(x) is monotonically increasing for values of x...

    Text Solution

    |

  2. The volume of the greatest cylinder which can be inscribed in a cone o...

    Text Solution

    |

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

    Text Solution

    |

  4. For all x in (0,1) (a) e^x<1+x (b) (log)e (1+x) < x (c) sin x > x ...

    Text Solution

    |

  5. Let A(p^2,-p),B(q^2, q),C(r^2,-r) be the vertices of triangle ABC. A p...

    Text Solution

    |

  6. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

    Text Solution

    |

  7. Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x...

    Text Solution

    |

  8. Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)...

    Text Solution

    |

  9. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then (a)k<3...

    Text Solution

    |

  10. Let f: \mathbb{R} rarr \mathbb{R} be a twice differentiable function s...

    Text Solution

    |

  11. Show that 5xlt=8sinx-sin2xlt=6x for 0lt=xlt=pi/3dot

    Text Solution

    |

  12. Discuss the number of roots of the equation e(k-xlogx)=1 for different...

    Text Solution

    |

  13. Prove that sin1>cos(sin1)dot Also, show that the equation sin("cos"(si...

    Text Solution

    |

  14. Pa n dQ are two points on a circle of centre C and radius alpha . The ...

    Text Solution

    |

  15. If f(x)=2/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^2+x+1)+(lambda^2-5...

    Text Solution

    |

  16. Let f(x)={(2-|x^2+5x+6|,x!=-2),(a^2+1,x=-2):} then value of 'a' so tha...

    Text Solution

    |

  17. If A >0,B >0 and A+B=pi/3, the maximum value of tanAtanB is

    Text Solution

    |

  18. f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasi...

    Text Solution

    |

  19. If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(''')(a)>0, then at x=a...

    Text Solution

    |

  20. The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot The...

    Text Solution

    |