Question

How do I solve lim((3x^3 - 5x +2)/(4x^2 + 3)) as x approaches infinity?

I divided everything by the largest power of x, but I ended up getting a denominator of 0. Do I have to factor this?

(answer is infinity)

Answer 1

Oh ok, thank you! My teacher taught us to divide by the largest power of x, so I didn't think of doing it like that.

But I don't quite get how c/0 is infinity. Isn't anything over 0 undefined?

Answer 2

You did fine.
When you get c/0, where c is non-zero,
then the limit will approach infinity

It might be easier to see if you divide everything by only x^2.

then lim((3x^3 - 5x +2)/(4x^2 + 3))
= lim (3x - 5/x + 2/x^2)/(4 + 3/x^2)

so as x approaches infinity you are left with 3x/4.
Now as x ---> ∞ the numerator 3x ---> ∞
and thus 3x/4 ----> infinity.