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Question

Solve:
limx2x243x2x+2

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Solution

limx2x243x2x+2

On rationalizing,

limx2x243x2x+2×3x2+x+23x2+x+2

limx2(x2)(x+2)[3x2+x+2]3x2x2

limx2(x2)(x+2)[3x2+x+2]2(x2)

=(2+2)2(4+4)=42×4

=8.

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