Can you help me understand limits and continuity in Calculus?

In summary: You might also be interested in this article on graphing limits.In summary, John is a high school senior who is interested in learning about math and physics. He struggles with staying awake during his teacher's classes due to the monotony and lack of excitement in the content. He would appreciate help with limits and continuity, and is looking for ways to learn these concepts on his own. He is also curious about how to create mathematical formulae on the website.
  • #1
marsbound2024
2
0
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.
 
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  • #2
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?
 
  • #3
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.
 
  • #4
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
 
  • #5
marsbound2024 said:
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) :wink:
 
  • #6
marsbound2024 said:
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:

[tex]\lim_{x\rightarrow{c}}f(x)=L[/tex]

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

Has your teacher gone over this definition?

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

[tex]\lim_{x\rightarrow{1}}\frac{x^2-1}{x-1}[/tex]

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

What is a limit?

A limit is a fundamental concept in calculus that represents the value that a function approaches as the input approaches a certain value.

How do you find limits?

Limits can be found by evaluating the function at various points around the input value and observing the trend of the outputs. Alternatively, you can use algebraic techniques such as factoring and rationalizing to simplify the expression and determine the limit.

What is the difference between left and right limits?

Left and right limits refer to the value that a function approaches from the left or right side of the input. Left limits are written as "lim x→a⁻" while right limits are written as "lim x→a⁺". If the left and right limits are equal, then the overall limit exists.

What is continuity?

Continuity is a property of a function where there are no sudden changes or breaks in the graph. This means that the function is defined at every point, and the limit at that point is equal to the function value at that point.

How do you determine if a function is continuous?

A function is continuous at a point if all three of the following conditions are met: 1) The function is defined at that point, 2) The limit at that point exists, and 3) The limit is equal to the function value at that point. If these conditions are met for all points in the function's domain, then the function is continuous.

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