Posted by **Stuck** on Saturday, February 6, 2010 at 3:04pm.

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)

- Math -
**Reiny**, Saturday, February 6, 2010 at 4:27pm
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.

- Math -
**Stuck**, Saturday, February 6, 2010 at 7:50pm
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 This Question

## Related Questions

- Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...
- Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...
- General Calculus Question - How do you solve a limit when it approaches infinity...
- limiting position of the particle - A particle moves along the x axis so that ...
- calculus - Help - I have three problems that I am stuck on - 1. Lim x approaches...
- Calc. Limits - Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0...
- calc - Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- ...
- Calc Please Help - Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/...
- Math: Limits - Estimate the limit numerically. lim as x→(approaches to)5 ...
- Calculus - how do you find the limit at infinity of: lim(x->infinity) (x+2)/...

More Related Questions