Posted by Anonymous on Wednesday, July 25, 2012 at 10:33pm.
Go on: wolframalpha dot com
When page be open in rectangle type:
limit x^3-2/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^3-2)/(x^2+x) as x---> -∞
= lim (x-1) + 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 x-1 as x -->-∞
which is -∞
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