Let f : R→[0, ∞) be such that limx→5 f(x) exists and limx→5 (f(x))2−9|x−5|=0. Then, limx→5 f(x) equals

Let f : R[0, ) be such that limx5f(x) exists and limx5(f(x))29|x5|=0. Then, limx5f(x) equals

  1. A

    1

  2. B

    2

  3. C

    3

  4. D

    0

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    Solution:

    limx5(f(x))29|x5|=0 limx5(f(x))29=0

       l2-9=0, where limx5 f(x)=l

      l=±3

      l=3                                          [ f(x)0 for all x  R]

      limx5 f(x)=3

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