SOLUTION: Solve as x approaches 0 lim ((x-2)^3 + 8)/x

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Question 937818: Solve as x approaches 0 lim ((x-2)^3 + 8)/x
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
lim%28x-%3E0%2C+%28%28x-2%29%5E3+%2B+8%29%2Fx%29+
so apply the l hospital rule and differentiate now the question can be written as
dy%2Fdx+=3%28%28x-2%29%5E2%29%2F1=> if x-%3E0 we have dy%2Fdx+=3%280-2%29%5E2 => dy%2Fdx+=3%2A4=12

lim%28x-%3E0%2C+%28%28x-2%29%5E3+%2B+8%29%2Fx%29=12+

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
limit as x approaches 0 of ((x-2)^3 + 8)/x is 12
(x-2)^3 = (x^3 -6x^2 +12x - 8) = x((x-6)x+12) -8
above result comes from factoring x
now we can return to our problem
limit as x approaches 0 of ((x-2)^3 + 8)/x = (x((x-6)x+12) -8 +8) / x = (x((x-6)x+12)) / x = ((x-6)x+12) = 12 as x approaches 0
above result comes from canceling x from numerator and denominator