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Limits

And no, not all functions have limits. I'll post more when I'm less lazy.

EDIT:

Okay, I'm less lazy all of a sudden.

Limits describe what the function does when taken to the extreme. In most cases, we're talking about positive and/or negative infinity.

Take a line equation, for example y=2x+1

As x approaches positive infinity, y (the value of the function) also approaches positive infinity. The limit of y=2x+1 as x approaches infinity is infinity.

Now take a regular sine wave y=sin(x)

The y value keeps oscillating between +1 and -1, regardless of how "extreme" x gets. Hence there is no limit to the function y=sin(x).

Post more questions as you have them.**subscribe**

EDIT 2:

This seems to be a pretty cool limit tutorial

Also, Google

And no, not all functions have limits. I'll post more when I'm less lazy.

EDIT:

Okay, I'm less lazy all of a sudden.

Limits describe what the function does when taken to the extreme. In most cases, we're talking about positive and/or negative infinity.

Take a line equation, for example y=2x+1

As x approaches positive infinity, y (the value of the function) also approaches positive infinity. The limit of y=2x+1 as x approaches infinity is infinity.

Now take a regular sine wave y=sin(x)

The y value keeps oscillating between +1 and -1, regardless of how "extreme" x gets. Hence there is no limit to the function y=sin(x).

Post more questions as you have them.

EDIT 2:

This seems to be a pretty cool limit tutorial

Also, Google

Last edited:

Check out the other links in my edit. That may help.

EDIT: (Sorry I keep doing this)

A limit is just a description of what*would* happen. So, yeah, you may be right depending on how you mean 'circle=limit'. If you keep increasing the number of sides to infinity, you get a circle. The circle is what would ultimately happen. And yes, the function is the number of sides to the shape, so f(x)=x-gon in this case.

EDIT: (Sorry I keep doing this)

A limit is just a description of what

Last edited:

- Nov 12, 2008

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Limits are largely useless, more so when you first learn them. They will make more sense once you go over derivitives and more when you go over intergration, so don't freak if they don't make sense yet.

A Limit is the value that a certain function approaches as x approaches some number. So consider the function y=(x^2-9)/(x-3) This function will look a lot like the function y=x+3 [(x^2-9)/(x-3) = ((x+3)(x-3))/(x-3) = (x+3)] However, it does not exist at x=3 [x-3=0, can't divide by 0]. However, we can describe what the function seems to be doing at three from what's happening around. [I apologize, but I don't feel like doing out a whole chart]. From the left, the graph seems to be going to 6 as x is going to 3, and the same from the right. The Graph will get impossibly close to 6 as x gets impossibly close to 3. Therefore, the LIMIT that they are approaching is 6.

A mental image you could use to imagine this is to imagine yourself moving along a graph [for this one, lets use y=(abs[x-3])/(x-3), abs[] means absolute value) from right to left (positive to negative). At x=3, that would be a cliff edge. If you stay at some point where x>3, you don't fall, and if you move to some point where x<3, you fall (in order for English to work properly, you don't want to fall). Because of this, your limit of motion is x=3. You can move up to this point, but you can not go past it, and if you stand on x=3, something weird happens. You have both fallen to and stayed at y=1. This is why it is said that y does not exist at x=3, but your limit of motion is three. (this specific example is would be the Limit as x approaches 3 from the right ["lim" with "x=3+" written under it]).

An important thing to watch out for is when the limit does not exist. This happens when there's oscillating behavior [like the limit of sin(x) as x approaches infinity], or the limit approaches two numbers from different directions [like y=(abs[x-3])/(x-3)]. Another thing to watch out for is when the function value is not the same as the limit. This is usually obvious (piecewise functions), but it can sometimes catch you. Make a habit of looking at the graph of a function when finding a limit (or have a mental picture of what the graph approximately looks like). If you have a line, and one point is not in that line, the limit is what the line approaches, not the stand alone point.

If I think of anything else, I'll edit it in here.

- Nov 12, 2008

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- Nov 12, 2008

- 14,153

- 1,334

- 0

- MBTI
- INFJ

- Enneagram
- 1w2 sx/so/sp

- Nov 12, 2008

- 14,153

- 1,334

- 0

- MBTI
- INFJ

- Enneagram
- 1w2 sx/so/sp

Calculus becomes fun when you use it in STATS!

Um no. I hate statistics just as much if not more then stats, and I have had to use calc-stats before. I detest all math unless it is applied to something revelent to me, then I can tollerate it.

You people can have stats. I just never got along with it...

Hey - has anyone else noticed that the surface area of a sphere ( = 4*pi*r^2 ) is the derivative of that sphere's volume ( = 4 / 3 * pi * r^3 )? And the circumference of a circle ( = 2 * pi * r ) is the derivative of that circle's area ( = pi * r^2 )? Connections...