If limx→∞ x2+1x+1−ax−b=2, then 

If limxx2+1x+1axb=2, then 

  1. A

    a =1, b = 3 

  2. B

    a=-1,b=3 

  3. C

    a =-1,b =-3 

  4. D

    a =1,b =- 3

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    Solution:

    We have,

    limxx2+1x+1axb=2

     limxx2(1a)x(a+b)+1bx+1=2      …(i)

    Since the limit of the given expression is a finite non-zero number. Therefore, numerator and denominator are of the same degree. 

     1a=0a=1

    Putting a = 1 in (i), we obtain

    limxx(1+b)+(1b)x+1=2 (1+b)=2b=3 

    Hence , a=1and b=-3 

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