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Question

Let f(x)={x2k(x24)2xwhen x is an int eger otherwise then limx2f(x)


A

exists only when k=1

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B

exists for every real k

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C

exists for every real k = 1

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D

does not exist

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Solution

The correct option is B

exists for every real k


limx2+f(x)=limx2+k(x24)2x =limx2+k(2x)=4klimx2+f(x)=limx2+k(x24)2x=limx2k(2x)=4k

Hence limits exists for every real value of k.


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