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duki
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Hi all,
Does anyone know of a couple of good links I could view that would explain limits?
Does anyone know of a couple of good links I could view that would explain limits?
duki said:Ok Great. I'll try to tell you what I understand and what I don't... sorry if it gets lengthy.
First off, I'm not sure what is even meant by "finding the limit". I'm not exactly a visual learner, but I do like to know what the equations are showing. Why is it called a limit?
One example of a problem I don't quite get is this:
[tex]lim as x->3 |x-3|/x-3[/tex]
The notes I have are it's und. at x = 3, x > 3 = +1, x < 3 = -1 and the ultimate answer is no limit. Why (especially the part about no limit)? Are these simple concepts that I shouldn't be having difficulties with?
We have gone over the basic limits:
1. [tex]lim b = b as x->constant[/tex]
2. [tex]lim x = c as x->constant[/tex]
3. [tex]lim x^n = c^n as x->c[/tex]
What do these mean? Where do the variables come from?
An example problem in my notes is as follows:
[tex]lim as x-> x^4 - x^3 + x - 1/ x^3 + 4x - 5[/tex]
so then you divide by x-1?? Not sure why you do that.
so after dividing you use synthetic division and get [tex]x^3 + 1[/tex]
apparently this is the final answer, but again... what does this show?
My main question I suppose is, when looking at a limit equation, how do you know where to start?
Many kudos for your help guys. :) Thanks!
ps) I'm not sure that I'm using the tex tags correctly.. sorry if I messed up.
duki said:Thanks a bunch for the help guys.
We're now working on problems with geometric functions:
[tex] lim x->3 tan(pi(x)/4) = -1[/tex]
but why?
duki said:Ok, we're starting to look at infinite limits.
To be honest, I'm completely confused here...
One of the examples is [tex]y=\frac{x}{x^2-5x+4}[/tex]
So we find the domain to be all reals where x is not 1 or 4... will this be the case for all equations like this? How do you know when to do it this way, and when to do it the other way, where a limit actually exists? How do you know when a limit doesn't exist?
Then the part comes to find the limits, which require four equations. How do you determine the limits from the negative approach and the positive approach to be infinity? How are these equations different from the previous examples?
Thanks for you patience! :)
A limit is a fundamental concept in mathematics that refers to the value that a function approaches as the input approaches a specific value. It is used to describe the behavior of a function near a certain point.
A limit and the value of a function at a specific point are not the same. The limit is the value that the function gets closer to as the input approaches a particular value, while the value of a function at a point is the actual output of the function when the input is that specific value.
There are three types of limits: one-sided, two-sided, and infinite limits. One-sided limits only consider the behavior of a function as the input approaches the specific value from one side. Two-sided limits consider the behavior of a function from both sides of the specific value. Infinite limits occur when the function approaches a positive or negative infinity as the input approaches a specific value.
Limits play a crucial role in determining the continuity of a function. If the limit of a function exists at a specific point, and the value of the function at that point is equal to the limit, then the function is continuous at that point. If the limit does not exist or is not equal to the value of the function, then the function is discontinuous at that point.
Limits have applications in various fields, including physics, economics, and engineering. For example, in physics, limits are used to describe the motion of objects, while in economics, they are used to understand the behavior of markets. In engineering, limits are used to calculate the rate of change of a system over time.