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Question

Evaluate limx(x2+5x+3x2+x+2)x=ea. Find a

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Solution

x2+5x+3x2+x+2=1+4x+1x2+x+2=1+y


Let y=4x+1x2+x+2=4x+1x21+1x+2x20 as x

Also

xy=4x2+xx2+x+2=4+1/x1+1x+1x24 as x

lim=limy0(1+y)x

=limy0[(1+y)1/y]xy=exy=e4 as xy4..........As limy0[(1+y)1/y]=e

a=4

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