Home
Class 11
MATHS
If lim(nrarrinfty)(an-frac(1+n^2)(1+n))...

If `lim_(nrarrinfty)(an-frac(1+n^2)(1+n))=b` a finite number then

A

a = 1, b= 1

B

a =1 , b= 0

C

a = -1 ,b= 1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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

value of underset(nrarrinfty)lim((n !)/n^n)^(1/n),where n inN is equal to

The integer n for which lim_(x rarr0)((cos x-1)(cosx-e^x))/x^n is a finite non-zero number is :

Discuss the continuity of the function, f(x)=lim_(nrarrinfty)(log(2+x)-x^(2n)sinx)/(1+x^(2n)) at x=1

If lim_(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to 4 (b) 1 (c) 2 (d) 3

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

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

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

The value of lim_(nrarrprop) ((n+1)(2n+1))/n^2 is

If the number of terms in the expansion of (a+x)^(n) is finite then n is a -

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If lim(xrarrinfty)(sqrt(x^2-x+1 )-ax-b) = 0 then the values of a and b...

    Text Solution

    |

  2. lim(xrarr0)[(In cosx)/((1+x^2)^(1/4)-1))] is equal to

    Text Solution

    |

  3. If lim(nrarrinfty)(an-frac(1+n^2)(1+n))=b a finite number then

    Text Solution

    |

  4. The integer n for which lim(x rarr0)((cos x-1)(cosx-e^x))/x^n is a fin...

    Text Solution

    |

  5. The value of lim(xrarrinfty)frac(x+cosx)(x+sinx is

    Text Solution

    |

  6. The value of f(0) so that the function f(x)=frac(2x-sin^-1x)(2x+tan^-1...

    Text Solution

    |

  7. Which of the following function has finite number of points of discont...

    Text Solution

    |

  8. Let f (x) = [3+2 cos x] , x in (-frac(pi)(2),frac(pi)(2)) where [.] de...

    Text Solution

    |

  9. If y = frac(1)(t^2-t-6 and t = frac(1)(x-2) then the values of x wh...

    Text Solution

    |

  10. The function f(x) = [x]^2-[x^2] (where [.] denotes the greatest integ...

    Text Solution

    |

  11. f + g may be continuous function, if

    Text Solution

    |

  12. If f(x) is continuous function AAx in R and the range of f(x) = (2, sq...

    Text Solution

    |

  13. Let f(x) be a continuous function defined for 1 le x le 3. If f(x) tak...

    Text Solution

    |

  14. If alpha, beta (alpha < beta) are the points of discontinuity of the f...

    Text Solution

    |

  15. If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...

    Text Solution

    |

  16. For a real number y, let [y] denotes the greatest integer less than or...

    Text Solution

    |

  17. If f(x)={(x^3, x gt 0),(0, x=0),(-x^3, x lt0):}

    Text Solution

    |

  18. Let h(x) = min {x, x^2}, x in R then h(x) is

    Text Solution

    |

  19. The set of all points where the functionf(x)= frac(x)(1+|x| is differe...

    Text Solution

    |

  20. Let f(x) = a+ b|x| + c|x|^4 where a, b and continuous are real constan...

    Text Solution

    |