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Question

Evaluate the limit:
limx01+x+x21x

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Solution

At x0,1+x+x21x becomes 00 form

On rationalising numerator, we get

=limx0(1+x+x2)(1+x+x2+1)x(1+x+x2+1)

=limx0((1+x+x2)212)x(1+x+x2+1)

[(ab)(a+b)=a2b2]

=limx0(1+x+x21)x(1+x+x2+1)

=limx0x(1+x)x(1+x+x2+1)[x0]

=limx0(1+x)(1+x+x2+)

=(1+0)(1+0+02+1)=12

limx01+x+x21x=12


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