## Limits and Continuity

Hello everyone:

I am a new member of this forum and this is my first post. I was referred by an Astronomy.com member and so I decided to check it out.

First I would like to introduce myself. My name is John and I am seventeen years of age and a senior in High School. My Calculus teacher also teaches Physics and I am also his aide. Thus I have him for five out of seven hours a day! He is one of the most monotone people I have ever met and the way he teaches is as if he expects us to know this stuff already.

Inevitably, I find myself drifting off to sleep during his classes but for recently I have managed to stay awake to learn about derivatives. However, I do need to learn a bit on limits and continuity. If anyone here could help me with these two sections of Calculus, I would be most grateful.

I have been interested in learning about math and physics for a long time until I got into his classes. He makes them so very boring. He's a nice person, but I feel his teaching is inadequate and his monotony could put an unruly baby to sleep.

Thanks again.

Sincerely, John C.
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 Welcome to PF. Limits in general is a pretty big section of Calculus. Is there something specifically that you want to learn or work on? Have you covered the delta-epsilon definition of a limit? Do you know different ways to go about determining limits (graphically, algebraically, etc)? Do you know how continuity or discontinuity affects a limit?

## Limits and Continuity

Well we are doing the delta "change-in" at the moment. So far we haven't had any problems with epsilon.

As far as what I am having trouble with is finding out if a limit is continuous or discontinuous and working related problems. It is quite annoying and yes I do find myself sleeping. I have read up on Calculus because I love to learn about it, but I still don't find myself able to put enough effort into the class itself. It is the graphing part that gets me sometimes, but I suppose the algebraic part is also confusing. If I come up with some example problems, I'll share.

I do have another question, however. How do you all create mathematical formulae on this website? Instead of me using something such as: x^2 times sqrt14 = 9, how do I create the graphical representations. I have seen it used commonly here. Thanks.

, marsbound2024

 Quote by marsbound2024 I do have another question, however. How do you all create mathematical formulae on this website? Instead of me using something such as: x^2 times sqrt14 = 9, how do I create the graphical representations. I have seen it used commonly here. Thanks. , marsbound2024
You can take a look at this thread for documents on the LaTex typesetting.

-
Navneeth (aka SN1987A)

 Quote by marsbound2024 Well we are doing the delta "change-in" at the moment. So far we haven't had any problems with epsilon.
The delta-epsilon I was referring to is the formal definition of a limit. If you're taking AP Calculus AB or BC, your teacher probably doesn't cover this because it's not on the exam. My teacher certainly didn't. I think it's important part of understanding what a limit is, so it could be beneficial to familiarize yourself with it.

It states:

$$\lim_{x\rightarrow{c}}f(x)=L$$

If for every number $$\epsilon >0$$ there is a number $$\delta >0$$ such that $$|f(x)-L| < \epsilon$$ whenever $$0<|x-c|< \delta$$

Has your teacher gone over this definition?

And, as a simple example of a limit involving discontinuity, here's one for you.

$$\lim_{x\rightarrow{1}}\frac{x^2-1}{x-1}$$

This can be done by various methods, but try it algebraically.

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