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Question

Evaluate the limit:
limx3x2x6x33x2+x3

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Solution

Given: limx3x2x6x33x2+x3 becomes 00 form

Using Factorization method

limx3x2x6x33x2+x3=limx3x23x+2x6x33x2+x3

limx3x(x3)+2(x3)x2(x3)+(x3)

limx3(x3)(x+2)(x3)(x21)

limx3(x+2)(x2+1)

=3+2(32+1)=510

=12

Therefore,

limx3x2x6x33x2+x3=12


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