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Question

Evaluate limx1(1x2+x2xx31)

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Solution

We need to find value of limx1(1x2+x2xx31)

=limx1(1(x1)(x+2)x(x1)(x2+1+x))=limx1{1(x1)(1x+2xx2+x+1)}=limx1{1(x1)(x2+x+1x22x(x+2)(x2+x+1))}=limx1{1(x1)(1x(x+2)(x2+x+1))}=limx11(x+2)(x2+x+1)=1(1+2)(1+1+1)=19


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