The value of limx→−∞ x2−x+1+x, is 

The value of limxx2x+1+x, is 

  1. A

    -12

  2. B

    12

  3. C

    1

  4. D

    -1

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    Solution:

    We have,

    limxx2x+1+x 

    =limyy2+y+1y, where y=x

    =limyy2+y+1yy2+y+1+yy2+y+1+y

    =limyy2+y+1y2y2+y+1+y=limyy+1y2+y+1+y=limy1+1y1+1y+1y2+1=12

    ALITER    limxx2x+1+x

    =limxx2x+1+xx2x+1xx2x+1+x=limxx2x+1x2x2x+1x=limxx+1x2x+1x

    =limxx|x|+1|x|x2x+1|x|x|x|             [ Dividing Nr and O' by x]

    =limxxx 1xx2x2x2+1x2+xxx2=|x|=x as x<0

    =limx11x11x+1x2+1=12

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