Home
Class 11
MATHS
("lim")(n→oo)(a n-(1+n^2)/(1+n))=b , whe...

`("lim")_(n→oo)(a n-(1+n^2)/(1+n))=b ,` where `a` is a finite number, then `a=1` (b) `a=0` (c) `b=1` (d) `b=-1`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If ("lim")_(xrarr0)({(a-n)n x-tanx}sinn x)/(x^2)=0, where n is nonzero real number, the a is 0 (b) (n+1)/n (c) n (d) n+1/n

The sum of first n odd natural numbers is 2n-1 (b) 2n+1 (c) n^2 (d) n^2-1

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

lim_(nrarr oo) (a^n_b^n)/(a^n+b^n) , where 1lt b lt a , is equal to

Let L=lim_(nrarroo)int_a^oo (ndx)/(1+n^2x^2) where a in R then cos L can be (A) -1 (B) 0 (C) 1 (D) 1/2

If lim_(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to (a) 4 (b) 1 (c) 2 (d) 3

("lim")_(n ->oo)[sum_(r=1)^n1/(2^r)],"where "[dot]" denotes G I F is equal to" (a) 1 (b) 0 (c) non existent (d) 2

Evaluate: lim_(n->oo)(-1)^(n-1)sin(pisqrt(n^2+0. 5 n+1)) ,where n in N

If lim_(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" epsilonN then the number of integers in the range of x is (a) 0 (b) 2 (c) 3 (d) 1

If lim_(x->0)(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

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If ("lim")(x->1)(2-x+a[x-1]+b[1+x]) exists, then a and b can take the ...

    Text Solution

    |

  2. Evaluate: ("lim")(n→oo)(n^p sin^2(n !))/(n+1)

    Text Solution

    |

  3. ("lim")(n→oo)(a n-(1+n^2)/(1+n))=b , where a is a finite number, then ...

    Text Solution

    |

  4. Evaluate: ("lim")(xvecoo)x^3{sqrt(x^2+sqrt(1+x^4))-xsqrt(2)}

    Text Solution

    |

  5. If m , n in N ,("lim")(xvec0)(sinx^n)/((sinx)^m)i s (a) 1, if n=m (b)...

    Text Solution

    |

  6. For any two complex numbers z1,z2 and any real numbers <math xmlns="ht...

    Text Solution

    |

  7. lim(n->oo)(-3n+(-1)^n)/(4n-(-1)^n) is equal to a. -3/4 b. 0 if n is...

    Text Solution

    |

  8. Evaluate : ("lim")(xvecoo)(sqrt(25 x^2-3x)+5x)

    Text Solution

    |

  9. Given a real-valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2)...

    Text Solution

    |

  10. Evaluate: lim(x-&gt;oo)((x^2+x-1)/(3x^2+2x+4))^((3x^2+x)/(x-2))

    Text Solution

    |

  11. L=(lim)(x-&gt;a)(|2sinx-1|)/(2sinx-1)dotT h e n limit does not exis...

    Text Solution

    |

  12. If [x] denotes the greatest integer less than or equal to x , then eva...

    Text Solution

    |

  13. f(x)=("lim")(n-&gt;oo)x/(x^(2n)+1)dotT h e n , A. f(1^+)+f(1^(-1))...

    Text Solution

    |

  14. Evaluate the limit: lim(x->1)((2x-3)(sqrt(x)-1))/(2x^2)

    Text Solution

    |

  15. ("lim")(x->oo)sum(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (...

    Text Solution

    |

  16. lim(x-&gt;1) (1+sin((3pix)/(1+x^2)))/(1+cospix) is (a) 0 (b) 1 ...

    Text Solution

    |

  17. f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim(x->oo)f(x) is equal...

    Text Solution

    |

  18. ("lim")(n vec oo)"{"(n/(n+1))^(alpha)+sin (1/n)]^n(when alpha in Q) i...

    Text Solution

    |

  19. The value of underset(xto2)lim(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))...

    Text Solution

    |

  20. If lim(n->oo)(n*3^n)/(n(x-2)^n +n*3^(n+1)-3^n) = 1/3 then the range of...

    Text Solution

    |