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Question

Let f(x)=x3+x216x+20(x2)2,if x2 k, if x=2 f f(x)be continuous for all x, then k =
  1. 7
  2. -7
  3. ±7
  4. None of these


Solution

The correct option is A 7
For continuous limx2f(x)=f(2)=k
k=limx2x3+x216x+20(x2)2
=limx2(x24x+4)(x+5)(x2)2=7

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