x-1/(x^2(x+2))

Describe the behavior to the left ad right of any vertical asymptote.

I'm using a computer other than my own (no access to mine), so I can't graph anything online.

Thanks.

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- Oct 17th 2007, 07:45 PMTruthbetoldDescribe the behavior
x-1/(x^2(x+2))

Describe the behavior to the left ad right of any vertical asymptote.

I'm using a computer other than my own (no access to mine), so I can't graph anything online.

Thanks. - Oct 17th 2007, 07:54 PMJhevon
- Oct 17th 2007, 08:46 PMTruthbetoldQuote:

well, you actually don't need the graph to tell what the behavior at the ends are. but if you want a graph, here it is. i assume the function is http://www.mathhelpforum.com/math-he...7f04ec6c-1.gif ...(you should use parentheses more efficiently)

Why did I want a graph? Oh, now I know why. Still, I need to be able to do it without a graph.

Thought:

Right hand: lim as x--> infinity f(x)/g(x) = 1

Left hand: lim as x--> - infinity f(x)/g(x) = 1

For the right, after expanding the equation

We have as the right,

Guess: and as the left, though no understanding how to prove, if even right.

Augh, this should be easy!!

Does it have to do with this?

**Definition**: A polynomial function (real) can be expressed in the form:

http://www.mathhelpforum.com/math-he...8b5fb309-1.gif

Our teacher, for some odd reason, didn't teach this, but it looks important since it was the first thing on the "Introduction to Calculus Tutorial" sticky on the Calculus board.

Thanks! - Oct 17th 2007, 09:07 PMJhevon