# Need LImit help!!!!!!!!!!

• Sep 29th 2012, 07:04 AM
ubhutto
Need LImit help!!!!!!!!!!
find the lim as x approaches positive and negative infinity

(3x^3 - x +1) / (x + 3)

• Sep 29th 2012, 07:07 AM
Prove It
Re: Need LImit help!!!!!!!!!!
Quote:

Originally Posted by ubhutto
find the lim as x approaches positive and negative infinity

(3x^3 - x +1) / (x + 3)

Start by dividing the top and bottom by x, to give

\displaystyle \begin{align*} \frac{3x^2 - 1 + \frac{1}{x}}{1 + \frac{3}{x}} \end{align*}

Then as you approach \displaystyle \begin{align*} \infty \end{align*} the top goes to \displaystyle \begin{align*} \infty \end{align*} and the bottom goes to 1, so the limit is \displaystyle \begin{align*} \infty \end{align*}.

Try evaluating the limit as you approach \displaystyle \begin{align*} -\infty \end{align*}...
• Sep 29th 2012, 07:11 AM
ubhutto
Re: Need LImit help!!!!!!!!!!
thanks

can you also show me how to get the horizontal asymptote of the graph
• Sep 29th 2012, 11:23 AM
HallsofIvy
Re: Need LImit help!!!!!!!!!!
Another way to do this to go ahead and divide: $\frac{3x^3- x+ 1}{x+1}= 3x^2- 3x+ 2- \frac{1}{x+1}$. As x goes to either + or - infinity, that last fraction goes to 0 so you only need to consider what happens to $3x^2- 3x+ 2$ determines the limit.

If you know what a "horizontal asymptote" is, you should realize that knowing the limit tells you everything you need to know about the horizontal asymptotes.