# What are the Limits of N* with c in Analysis?

• Shackleford
In summary, the conversation discusses the difficulty of reading a scanned photo of a math problem and suggests entering the text instead. The speaker also mentions the solution to a problem in class and provides a clear photo of another problem.
Shackleford
I'm not sure about my work.

N = neighborhood
N* = deleted neighborhood
c = accumulation point

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20111011_224646.jpg

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20111011_224704.jpg

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The first one looks fine, but here's a simpler counterexample:
$$f(x) = \left\{ \begin{array}{l l} 1 & \quad \mbox{x = 1}\\ 0 & \quad \mbox{otherwise}\\ \end{array} \right.$$

For the other one, your scan is so dark and of such poor quality that I can't read it.

Mark44 said:
For the other one, your scan is so dark and of such poor quality that I can't read it.

You should be able to zoom in. If that doesn't work, I'll take another picture.

Shackleford said:
You should be able to zoom in. If that doesn't work, I'll take another picture.
It's also difficult to read your writing. It would be better if you just entered what you have as text.

Frankly, if you want us to help with your work, it behooves you to make it as easy as possible for us to do so. Whenever someone posts a picture of their work, and I have to click a link to see a scanned photo of it, I really don't feel much like putting in a lot of effort to decipher what's there.

The professor worked the second problem in class today. I had the the right idea, but he did it a bit more rigorously.

This next picture should be clear enough. I said this is false.

http://i111.photobucket.com/albums/n149/camarolt4z28/rsz_img_20111012_151514.jpg

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## What is the meaning of "Analysis: Limits of N* w/ c"?

The phrase "Analysis: Limits of N* w/ c" refers to a mathematical concept known as the limit. It involves evaluating the behavior of a function as its input approaches a certain value, often denoted as "N", while taking into account a constant value, denoted as "c".

## What is the purpose of studying limits?

The study of limits is essential in understanding the behavior of functions and their graphs. It allows us to determine the behavior of a function at a specific point, such as whether it approaches a certain value or becomes infinite. Limits also play a crucial role in calculus and other branches of mathematics.

## How are limits calculated?

Limits are typically calculated using algebraic manipulation and substitution. However, for more complex functions, other techniques such as L'Hopital's rule or the squeeze theorem may be used. The ultimate goal is to evaluate the limit by determining the value that the function approaches as its input gets closer and closer to the given value.

## What are the common types of limits?

The most common types of limits include one-sided limits, where the function is evaluated from only one direction, and two-sided limits, where the function is evaluated from both sides. Other types include infinite limits, where the function approaches positive or negative infinity, and limit at infinity, where the input value approaches infinity.

## What are the applications of limits in real life?

Limits have various applications in real life, including physics, engineering, and economics. In physics, limits are used to calculate velocity and acceleration. In engineering, limits are used to design structures that can withstand extreme conditions. In economics, limits are used to determine optimal production levels and supply and demand.

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