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Question

The value of limx0 1+x21x2x is

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Solution

limx0 1+x2 1x2x=limx0 1+x2 1x2x×1+x2 + 1x21+x2 + 1x2=limx0 (1+x2)2 (1x2)2x(1+x2 + 1x2)=limx0 (1+x2) (1x2)x(1+x2 + 1x2)=limx0 1+x21+x2x(1+x2 + 1x2)=limx0 2x2x(1+x2 + 1x2)=limx0 2x1+x2 + 1x2=0

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