Lim x→3 [8x/ (x−3)^2 ] Why does the result is infinity positive?

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I can't find why to resolve the question. Help me!

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Answer 1 · 2018-04-20T04:05:02

Please see below.

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#Lim_(x->3)(8x)/(x-3)^2=Lim_(x->3)(8x)/((1-3/x)x)^2=Lim_(x->3)(8x)/((1-3/x)^2x^2)=8*Lim_(x->3)1/((1-3/x)^2x#

For #x# approaching #3# from the right, #(1-3/x)^2x > 0#. As such. the denominator is positive. Therefore,

#8*Lim_(x->3)1/((1-3/x)^2x)=8*oo=oo#