Can you help me understand limits and continuity in Calculus?

[marsbound2024]

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.

John C.

 

[Jameson]

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?

 

[Woozie]

Quick suggestion: If you can't follow your teacher because he is too boring then it may be beneficial to study ahead of the class.

Last year, as a senior in high school, I was also an assistant to my calculus teacher. English was her second language so she had an accent that made her hard to understand. Luckily, I had already taught myself calculus so not understanding her was no problem.

I also had a friend who always studied a few sections ahead of the teacher so he could just sleep in class and not worry too much about what he missed.

And remember, if you ever need help on anything, or if your willing help other people out on their work you can always come to PF's.

 

[marsbound2024]

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

 

[neutrino]

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.
https://www.physicsforums.com/showthread.php?t=8997

Enjoy your stay here!

-
Navneeth (aka SN1987A)

 

[Jameson]

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.