Home
Class 12
MATHS
Compare which of the two is greater (100...

Compare which of the two is greater `(100)^(1/100) and (101)^(1/101)`

Text Solution

AI Generated Solution

To compare \( (100)^{1/100} \) and \( (101)^{1/101} \), we can define a function and analyze its behavior. Let's go through the steps systematically. ### Step 1: Define the function Let \( f(x) = x^{1/x} \). ### Step 2: Find the natural logarithm To analyze the function, we take the natural logarithm: \[ ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Self Practice Problems|36 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise -1A|5 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

Similar Questions

Explore conceptually related problems

Find the greater number is 100^(100) and (300)!.

Which is larger : (99^(50)+100^(50)) or (101)^(50) .

Find the greater of the two number: (1.01)^1000000 and 10000

Which number is larger (1.01)^(1000000) or 10,000 ?

Use binomial theorem to evaluate (10.1)^(5) .

compared to burn due to air at 100^(@) a burn due to steam at 100^(@)C is

If the mean deviation of the numbers 1,""1""+""d ,""1""+""2d ,""..."",""1""+""100 d from their mean is 25, then the d is equal to (1) 10.0 (2) 20.0 (3) 10.1 (4) 20.2

The sum of the series (.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100)) is "____" .

The number of zeros at the end of (101)^(11)-1 is

If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2) the value of x^(100)+y^(100)+z^(100)-(9)/(x^(101)+y^(101)+z^(101)) is

RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. Compare which of the two is greater (100)^(1/100) and (101)^(1/101)

    Text Solution

    |

  2. A particle moving on a curve has the position at time t given by x=f'(...

    Text Solution

    |

  3. Find the interval in which f(x) = xsqrt(4ax-x^2), (alt0) is decreasing

    Text Solution

    |

  4. If the function f:[0,4]vecR is differentiable, the show that for a , b...

    Text Solution

    |

  5. if all the function f(x)=a^2x^3-a/9x^2-2x-b arepositive and the minimu...

    Text Solution

    |

  6. if f(x) = {underset(a^(2) -2+ (sin (x-K))/(x-K))(3+|x-k|)," "underse...

    Text Solution

    |

  7. The equation x^3-3x+[a]=0, where [*] denotes the greatest integer func...

    Text Solution

    |

  8. Let f(x) =sin ({x})/(a) + cos ({x})/(a) where a gt 0 and {.} denotes t...

    Text Solution

    |

  9. A function f(x) having the following properties, (i) f(x) is conti...

    Text Solution

    |

  10. A figure is bounded by the curves y=x^2+1, y=0,x=0,a n dx=1. At what p...

    Text Solution

    |

  11. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,\ -1) , find the val...

    Text Solution

    |

  12. if A be the area of a triangle, prove that the error in A resulting fr...

    Text Solution

    |

  13. Find the possible values of a such that the inequality 3-x^(2)gt|x-a| ...

    Text Solution

    |

  14. lf f'(x) > 0,f"(x)>0AA x in (0,1) and f(0)=0,f(1)=1,then prove that...

    Text Solution

    |

  15. Find the interval of increase and decrease for the function g(x) =...

    Text Solution

    |

  16. The interval to which a may belong so that the function f(x)=(1-(sqrt(...

    Text Solution

    |

  17. Find positive real numbers 'a' and 'b' such that f(x) =ax-bx^(3) has...

    Text Solution

    |

  18. For any acute angled triangleABC,(sinA)/(A)+(sinB)/(B)+(sinC)/(C ) can

    Text Solution

    |

  19. Find the minimum value of f(x) =8^(x) +8^(-x) -4(4^(x)+4^(-x)) , AA x ...

    Text Solution

    |

  20. Show that height of the cylinder of greatest volume which can be in...

    Text Solution

    |

  21. The cosine of the angle at the vertex of an isosceles triangle having ...

    Text Solution

    |