Posted by Jessica on Thursday, June 21, 2012 at 1:43pm.
do you mean x --> -1? Otherwise, there's no problem evaluating the fraction.
x^3+1 = (x+1)(x^2-x+1)
divide out the (x+1) to get
limit = 3
or, using L'Hopital's rule,
lim (3x^2)/1 = 3
x^2(3-x) / x^2(x+4) = (3-x)/(x+4) --> 3/4
lim (16-x)/(√x-4) = lim (-1)/(1/(2√x)) = -1/(1/8) = -8
or, divide out the √x-4, since 16-x = -(√x-4)(√x+4) --> -8
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