Question

can someone please explain why the answer to this is negative infinity? I keep getting positive.

lim
x--> - infinity x^3-2/x^2+x

Answer 1

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.

Answer 2

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 -∞