Horizontal Asymptote

[Ergot]

Where is it when y = 3x / (x+3)^2 ?

[dark_drake]

y = 0

At least if I remember correctly.

[Ergot]

Explain :( ?

[dark_drake]

The limit as x approaches +infinity and -infinity is 0.

[Sidoh]

Explain :( ?

Actually, there's a really easy way to do this problem (without graphing or anything).

Since the total powers of x (2) are greater in the denomonater than they are in the numerator, f(x) will approach 0 as x approaches infinity.  This is always the case with any function, no matter how big a constant on either may be.  Conversely, if the powers of x are larger in the numerator than in the demononator, f(x) will approach infinity.

[dark_drake]

Explain :( ?

Since the total powers of x (2) are greater in the denomonater than they are in the numerator, f(x) will approach 0 as x approaches infinity.  This is always the case with any function, no matter how big a constant on either may be.  Conversely, if the powers of x are larger in the numerator than in the demononator, f(x) will approach infinity.

This is true; however, learning the limit thing is useful for when the powers are equal.  As always, I reccomend learning the basics and using shortcuts after growing comfortable with the basics.

[Ergot]

Thanks... I have a quiz on this tomorrow, hopefully he'll leave those types out...
drake... explain the basic to me? AFAIK, this will get me pretty far until I learn more in calc or w/e.

[dark_drake]

Thanks... I have a quiz on this tomorrow, hopefully he'll leave those types out...
drake... explain the basic to me? AFAIK, this will get me pretty far until I learn more in calc or w/e.

Just the limit as x approaches plus and minus infinity. How you do that, at least how I learned, is about like this:


Basically, you can't evaluate the limit of the function as x approaches infinity because when you plug infinity in, you get infnity/infinity, which is undefined.  So, you have to divide the numerator and denominator by the largest power of x.

Edit: This only works if the powers in the denominator are >= those in the numerator.  If the numerator's are greater, you're dealing with slant asymptotes.

[Ergot]

I SEE !!!

[rabbit]

Or when it's undefined (IE: -3).

[Ergot]

Or when it's undefined (IE: -3).

That would be x = -3 or the vertical asymptote... that one is easy.

[rabbit]

Fuck asymptotes, I'm done with high school!

[MyndFyre]

Thanks... I have a quiz on this tomorrow, hopefully he'll leave those types out...
drake... explain the basic to me? AFAIK, this will get me pretty far until I learn more in calc or w/e.

Just the limit as x approaches plus and minus infinity. How you do that, at least how I learned, is about like this:


Basically, you can't evaluate the limit of the function as x approaches infinity because when you plug infinity in, you get infnity/infinity, which is undefined.  So, you have to divide the numerator and denominator by the largest power of x.

Edit: This only works if the powers in the denominator are >= those in the numerator.  If the numerator's are greater, you're dealing with slant asymptotes.

Easier way to do that limit: L'Hospital's Rule. 



Really handy, because it can be applied several times.  For example, you want to find the limit of the following function:


So, as a good, easy mneumonic device:

1.) If the exponent of the numerator is greater, the function will have a limit of +infinity or -infinity.
2.) If the exponent of the denominator is greater, the function will have a limit of 0.  Series defined by this function will be convergent.
3.) If the exponents of the numerator and denominator are the same, the limit will be a constant of the numerator's greatest-power coefficient times the factorial of the power, divided by the denominator's greatest-power coefficient times the factorial of the power (in the example it was 6*5!/12*5!).  I believe that the series will be convergent, but I can't remember for sure.

Also, limits don't need to be taken to infinity.  They can be found at any point along the function.

[Ergot]

Uhh... I don't understand that :( I'm only in Algebra II.

[deadly7]

What the hell do factorials have to do with this?  You have weird ways of doing things.. graphing takes about two seconds with a calculator and is way easier.