calculus
posted by Anonymous on .
can someone please explain why the answer to this is negative infinity? I keep getting positive.
lim
x>  infinity x^32/x^2+x

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. 
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 ∞