My Experience..

Tell my friend about Limit Function

On 9th january 2009, I try to explain the material of mathematic to my friend. My friend is Alin. She is my classmate. I tell her about Limit. In senior high school ,we have got this material. So ,she know less about limit. First, I tell her the definition limit function. I tell,” Function f is defined at opened interval that having a, maybe at a have no value definition. Limit f(x) is L for x approach a,can be written:

Lim f(x) =L “.

x-->a

then I tell her about the postulates of limit, I just tell her a part of them. It’s just a introduction to learn about limit. So I don’t explain her of all the limit. In process I explain the limit, we always laughing together. And I try to be serious. I try to think that my friend is the students, and I am the teacher. I can explain easily, because she can catch my explain fast. After I tell her, I give her some exercises. I give her five exercises, and she can do three well, but not of two numbers. Then I give the explaining for her to get the correct answer. So, she can catch my explaining clearly now. I try not to be the real teacher for her, I just try to explain her, and we enjoy it. We learn together. Learn about limit.
From this moment, I can do the activity that can make my friend be clearly in limit. From she know about limit, now she more be professional (hehehe..just kidding..). And this is my experience. Try to be the great teacher (without angry…hehehe..).
This is my experience, maybe I’m not a perfect person..sorry I mean that I’m not the great teacher. And thanks for viewing my blog or thanks for reading.

The concept of limit:
Limit concept of limit is fundamental in understanding the differential calculus and integral calculus,that one of kinds of mathematics.
Definition
Function f is defined at opened interval that having a, maybe at a have no value definition. Limit f(x) is L for x approach a,can be written:
Lim f(x) =L
x-->a
If for every positive number ε, however so tidy will be got positive number δ, so
|f(x) – L| < ε is followed by 0 < |x – a| < δ

The Postulates
Postulate 1

If m and b are constanta, so

Lim (mx+b) = ma +b
x-->a

Postulate 2
If c is constanta, so for every arbitrary number a
Lim c =c
x-->a

Postulate 2
Lim x = a
x-->a

Postulate 4
If lim f(x) =L and lim g(x)= M, so
x-->a x-->a
lim [f(x) + g(x)] = L+M
x-->a

Postulate 5
If lim f(x) =L and lim g(x)= M, so
x-->a
lim [f(x) . g(x)] = L.M
x-->a

Postulate 6
If lim f(x) =L and n is arbitrary positive number, so
x-->a
lim [f(x)]^n = L^N

Postulate 7
If lim f(x) = L and lim g(x) = M, and M is not 0, so
x-->a x-->a
lim [f(x) / g(x)]= L/M
x-->a

The Right Limit and Left Limit

Definition
Function f is defined for every number at interval (a,c). So limit f(x) for x approach a from the right is R. can be write:

Lim f(x) = R
x-->a+

if for every positive number ε, however so tidy will be got positive number δ . so ;
|f(x) – R| < ε is followed by 0 < |x – a| < δ

Definition
Function f is defined for every number at interval (d,a). So limit f(x) for x approach a from the left is L. can be write:

Lim f(x) = L
x-->a-

if for every positive number ε, however so tidy will be got positive number δ . so ;
|f(x) – L| < ε is followed by 0 < |a-x| < δ

By the definition of left and right limit, so, all of postulates that have learn before is used for right limit and left limit.

Source: “Kalkulus I.by Drs.Soemoenar”