Limits, differentiation, related rates, integration, trig integrals, etc.
rowdy3
Posts: 6
Joined: Tue May 04, 2010 11:51 pm
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Please determine the following limit if they exist. If the limit doe not exist put DNE.

lim 2x^3 / x^2 + 10x - 12

x->infinity.

Thanks.

Stranger_1973
Posts: 21
Joined: Sun Feb 22, 2009 9:56 pm

You can use asymptotes from algebra: http://www.purplemath.com/modules/asymtote.htm

Since the degree of the numerator is more than the degree of the denominator, it has to 'go to infinity', so 'the limit does not exist'.

Hope that he,lps.

Martingale
Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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rowdy3 wrote:Please determine the following limit if they exist. If the limit doe not exist put DNE.

lim 2x^3 / x^2 + 10x - 12

x->infinity.

Thanks.

$\lim_{x\to\infty}\frac{2x^3 }{x^2 + 10x - 12}=\lim_{x\to\infty}\frac{2x^3 }{x^2 + 10x - 12}\cdot\frac{1/x^2}{1/x^2}=\lim_{x\to\infty}\frac{2x }{1 + 10/x - 12/x^2}$

here the bottom goes to 1 and the top goes to infinity. So the limit is infinity (or DNE if that's what your instructor wants)