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Question

Evaluate the following:
limx1x23x+2x24x+3limx2x3+x212x3x2x2limx2x2+x24x23x2+4limx3x33x2x+3x36x2+9x

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Solution

Use L-Hospital rule
limx1x23x+2x24x+3=limx12x32x4=2(1)32(1)4=12

limx2x3+x212x3x2x2=limx23x2+2x3x22x1=3(4)+2(2)3(4)2(2)1=167

limx2x2+x24x23x2+4=limx22x+22x32=2(2)+22(2)(32)=3

limx3x33x2x+3x36x2+9x=limx33x26x13x212x+9=6x66x12=2.

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