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Question
Let f(x)={x2k(x24)2xwhen x is an int eger otherwise then limx2f(x)
Options:
A .  exists only when k=1
B .  exists for every real k
C .  exists for every real k = 1
D .  does not exist
Answer: Option B
:
B
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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