If limx→−∞ x2−x+1−ax−b=0, is 

If limxx2x+1axb=0, is 

  1. A

    a=1,b=12

  2. B

    a=1,b=12

  3. C

    a=1,b=12

  4. D

    none of these

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    Solution:

    We have, 

    limxx2x+1(ax+b)=0limxx2x+1(ax+b)2x2x+1+(ax+b)=0limxx21a2x(1+2ab)+1b2x2x+1+ax+b=01a2=0 and 1+2ab=0a=±1 and b=1/2.

    For a=1 and b=1/2 we observe that  

    limxx2x+1axb=limxx2x+1+x12

    Hence, a=1 and b=12

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