limx→−1 x4+x2+x+1×2−x+11−cos⁡(x+1)(x+1)2 is equal to

limx1x4+x2+x+1x2x+11cos(x+1)(x+1)2 is equal to

  1. A

    1

  2. B

    2/3

  3. C

    3/2

  4. D

    e1/2

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    Solution:

    We observe that

    x4+x2+x+1x2x+123 as x11cos(x+1)(x+1)200 as x1.limx1x4+x2+x+1x2x+11cos(x+1)(x+1)22sin2x+1=23x11cos(x+1)lim(x+1)2=23limx124x+122=231/2

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