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Question

Evaluate limx2f(x) (if it exists), where f(x)

=x[x],x<24,x=23x5,x>2


Solution

limx2f(x)=limx2{x[x]}

=limx2xlimx2[x]

=21=1[limxk[x]=k1]

limx2+f(x)=limx2+(3x5)

=3(2)-5

=6-5

=1

Thus,limx2f(x)=1=limx2+f(x)

limx2f(x)=1

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