I've done Calculus long time ago But now again I am doing it

[Moni]

I've done Calculus long time ago! But now again I am doing it seriously to become an expert on it :)

And what I emphasise is the underlying ideas, not just doing maths :(

So, what I want to discuss first, about LIMIT.

How the concept of Limit came from? why it's always x -> 0...type? what's these delta, epsilons? And why this is defined so complexly ?

 

[mathman]

The concept of limit took a long time to develop, and it has a rather complex history. I suggest trying google.

It is NOT always x->0. It can be x-> anything. The epsilon delta approach was developed in the nineteenth century to give a mathematically rigorous foundation to the idea. Once you get the hang of it, it isn't so bad.

 

[PrudensOptimus]

Originally posted by Moni
I've done Calculus long time ago! But now again I am doing it seriously to become an expert on it :)

And what I emphasise is the underlying ideas, not just doing maths :(

So, what I want to discuss first, about LIMIT.

How the concept of Limit came from? why it's always x -> 0...type? what's these delta, epsilons? And why this is defined so complexly ?

limit f(x) = what f(x) approaches as x approaches 0, infinity, ... whatever etc...

 

[Moni]

Thanks MathMan!
I've read books in my classes, but those are all full of Typical examples and theories!

Google isn't helping much :(

Then limit is open interval in one side ?

 

[Moni]

Originally posted by PrudensOptimus
limit f(x) = what f(x) approaches as x approaches 0, infinity, ... whatever etc...

Aha! Chinese Man has started showing his Kung Fu in the field of Calculus

I'm in difficulty with Approaches !

 

[PrudensOptimus]

Originally posted by Moni
Aha! Chinese Man has started showing his Kung Fu in the field of Calculus

I'm in difficulty with Approaches !

Heh, you are a funny guy bud.

Approaches is a concept that takes a while to understand, when I first see limit... I cogitated on it for about 4 weeks, until I get a real understanding of it.

x-->0, meaning x = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001...

x-->infinity, meaning x = 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!

suppose L = Limit(x-->0) f(x), where f(x) is the function graph, as x--->0, something really small and close to 0--f(x) is approaching L.

 

[Moni]

Originally posted by PrudensOptimus
Heh, you are a funny guy bud.

Approaches is a concept that takes a while to understand, when I first see limit... I cogitated on it for about 4 weeks, until I get a real understanding of it.

x-->0, meaning x = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001...

x-->infinity, meaning x = 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!

suppose L = Limit(x-->0) f(x), where f(x) is the function graph, as x--->0, something really small and close to 0--f(x) is approaching L.

Asian man we all are Asian! We know each others culture ;)

Hmm...if Limit is what you are talking...then why it's said in the books that it has great impact on the world of Calculas !

At least what I've done in my classes ... just solving problms :(
And there I found no uses of Limit

 

[PrudensOptimus]

Originally posted by Moni
Asian man we all are Asian! We know each others culture ;)

Hmm...if Limit is what you are talking...then why it's said in the books that it has great impact on the world of Calculas !

At least what I've done in my classes ... just solving problms :(
And there I found no uses of Limit

Limit is usually a prelude to Derivates(rate at something changes).

Derivative is basically y/x, as x becomes really really really small, really close to 0, but not 0.

 

[IceZero]

Limits actually came before derivatives, and they helped determine many algorithms for differentiating problems, such as product rule, quotient rule, chain rule, etc...If those rules were not around, we would still be doing the limit of a function as the function approaches something...I think that would be very tedious and hard...But the purpose of a limit is that it also helps us come up with new algorithms of problems that are unsolvable with regular derivative rules...

One example to show the use of limits is trig... Trig functions do not obey regular differentiation rules, therefore in order to explain why the derivative of sin(x) is cos(x)...We use limits to see how a graph behaves as it approache a certain given value or interval... See the proof for the derivative of sin(x) or cos(x) to see what I mean...Even logarithms have their own algorithms for differentiating...But all these algorithms were developed through the use of limits...and of course integrals...We can't forgot those.