Home
Class 12
MATHS
Let for all xgt0, f(x)=lim(nrarroo)n(x^(...

Let for all `xgt0, f(x)=lim_(nrarroo)n(x^((l)/(n))-1)`, then

A

`f(x)+f((1)/(x))=1`

B

`f(xy)=f(x)+f(y)`

C

`f(xy)=xf(y)+yf(x)`

D

`f(xy)=xf(x)+yf(y)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2016

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|75 Videos

  • QUESTION PAPER 2018

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|75 Videos

Similar Questions

Explore conceptually related problems

Let for all xgt0,f(x)=lim_(nto oo)n(x^((1)/(n))-1) , then

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then f has

Evaluate the following limits : lim_(nrarrinfty)n(x^(1/n)-1) , xgt0

If f(x)=lim_(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal to

If phi(x)=lim_(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n)) , then

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

If f(x)=lim_(ntooo)(x^(n)g(x)+h(x))/(x^(n)+1) show that f(x) =h(x), when 0ltxlt1 =(1)/(2)[h(x)+g(x)] , when x=1 =g(x), when xgt1

Let f(x)=lim_(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5) . Then the set of values of x for which f(x)=0 is

Prove that lim_(xrarr0) ((1+x)^(n) - 1)/(x) = n .

Discuss the continuity of f(x)=(lim)_(n->oo)(x^(2n)-1)/(x^(2n)+1)

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2017-Multiple Choice Questions
  1. Let A(-1,0) and B(2,0) be two points. A point M moves in the plane in ...

    Text Solution

    |

  2. If f(x)=int(-1)^(x)|t|dt, then for any xge0.f(x) is equal to

    Text Solution

    |

  3. Let for all xgt0, f(x)=lim(nrarroo)n(x^((l)/(n))-1), then

    Text Solution

    |

  4. Let l=int(0)^(100pi)sqrt((1-cos2x))dx, then

    Text Solution

    |

  5. The area of the figure bounded by the parabolas x=-2y^(2) and x=1-3y^(...

    Text Solution

    |

  6. Tangents are drawn to the ellipse (x^(2))/(9)+(y^(2))/(5)=1 at the end...

    Text Solution

    |

  7. The value of K in order that f(x)=sinx-cosx-Kx+5 decreases for all pos...

    Text Solution

    |

  8. For any vector vecx. Then value of (vecx xx hati)^(2)+(vecx xx hatj)^(...

    Text Solution

    |

  9. If the sum of two unit vectors is a unit vector. Then the magnitude of...

    Text Solution

    |

  10. Let alpha and beta be the roots of x^(2)+x+1=0. If n be positive integ...

    Text Solution

    |

  11. For real x, the greatest value of (x^(2)+2x+4)/(2x^(2)+4x+9) is

    Text Solution

    |

  12. Let A=((1,1,1),(0,1,1),(0,0,1)). Then for positive integer n. A^(n) is

    Text Solution

    |

  13. Let a, b, c be such that b(a+c)ne0. If |(a,a+1,a-1),(-b,b+1,b-1),(c,...

    Text Solution

    |

  14. Let f: R rarr R be twice continuously differentiable. Let f(0)=f(1)=f'...

    Text Solution

    |

  15. If f(x)=x^(n), n being a non-negative integer, then the values of n fo...

    Text Solution

    |

  16. Let f be a non-constant continuous function for all xge0. Let f satisf...

    Text Solution

    |

  17. If the line ax+by+c=0,abne0, is a tangent to the curve xy=1-2x. Then

    Text Solution

    |

  18. Two particles move in the same straight line starting at the same mome...

    Text Solution

    |

  19. The complex number z satisfying the equation |z-i|=|z+1|=1 is

    Text Solution

    |

  20. On R, the set of real numbers, a relation rho is defined as 'a rhob if...

    Text Solution

    |