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Question

Find the following limit.
limx0(1+x)(x+2x)(1+3x)1x.

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Solution

limx0(1+x)(1+2x)(1+3x)1x
=limx0(1+2x+x+2x2)(1+3x)1x
=limx0(1+3x+2x2)(1+3x)1x
=limx0(x+3x+2x2+3x+9x2+6x3)1x
=limx06x2+11x2+6xx
6x(6x2+11x+6)x
=6.

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