Question

What are "limits at finite points" ?

Answer 1

If you aren't willing to "waste time" don't, and don't span the thread!

Answer 2

(slowly!)

Answer 3

Limits that approach a finite point in the domain, as opposed to infinity.

Answer 4

yes they are finite, .... and what

Answer 5

not really that well posed
a function can have and infinite number of limit points

Answer 6

That would be something like: find the limit as x approaches 5
As contrasted with: find the limit as x approaches infinity

Answer 7

What more do you want? You'll need to be more specific.

Answer 8

can someone work an example with me, (if you have time)

Answer 9

Do you have an example problem?

Answer 10

Nope!

Answer 11

Okay, let's consider the function \[
f(x)=\frac {x^2}x
\]Now you would think that \[
f(x)=x
\]However, this is not completely true. Unlike \(x\), \(x^2/x\) can't be defined at \(x=0\).

Answer 12

So suppose \(g(x)=x\). We can say \(g(0) = 0\), but \(f(0)\) is not defined.

Answer 13

If you tried to evaluate it, you would get \[
f(0) = \frac {0^2}0 = \frac 00
\]This is an indeterminate form. If we let \(0/0=n\):\[
\frac 00 =n \implies 0=0n
\]So we could say \(n=5\) or \(n=2\) and this equation would still hold. Any number is a potential candidate, thus it is indeterminate.

Answer 14

Now if you put in very small numbers into \(f(x)\) such as \(f(0.0001)\) you will notice that it gets really close to \(0\). In fact it is approaching what \(g(0)\) is equal to.

The concept of a limit to figure out what a function approaches instead of how the function is actually defined.

Answer 15

We write this as:\[
\lim_{x\to 0}f(x) = 0
\]