Posted by Anonymous on Wednesday, July 25, 2012 at 10:33pm.
can someone please explain why the answer to this is negative infinity? I keep getting positive.
lim
x>  infinity x^32/x^2+x

calculus  Bosnian, Wednesday, July 25, 2012 at 10:56pm
Go on: wolframalpha dot com
When page be open in rectangle type:
limit x^32/x^2+x as x>  infinity
and click option =
After few seconds when you see result click option:
Show steps
On wolfram alpha dot com you can practice any kind of calculus.
That is good just for practice.
You can't use wolframalpha on exam.

calculus  Reiny, Thursday, July 26, 2012 at 8:18am
Just get a feel for the numbers
x >  infinity
for very large negative numbers , x^3  2 becomes "
"hugely negative"
but x^2 + x becomes + "very large"
since /+ =  , and the numerator is larger than the denominator by a factor of x,
the answer is negative infinity
or
(x^3  2)/(x^2 + x) = x  1 + (x+2)/(x^2+x)
lim (x^32)/(x^2+x) as x> ∞
= lim (x1) + lim (x+2)/(x^2+x) as x> ∞
since intuitively we can see that lim (x+2)/(x^2+x) > 0 as x > ∞
we are left with lim x1 as x >∞
which is ∞
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