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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2013-05-23 03:37:05

Hi;

It is a nice link, alot of good explanation there.

{7/3}
2013-05-22 23:31:55

Thanks,bobbym,my friend liked the proof and i liked the link.

bobbym
2013-05-22 18:57:34

Hi;

This is what I use, maybe he will like it.

http://www.milefoot.com/math/calculus/l … oofs04.htm

{7/3}
2013-05-22 13:32:03

I think he wants proof of the composition law

bobbym
2013-05-22 13:06:01

Hi;

Use the composition law for limits:

If x is continuous at b and



then

{7/3}
2013-05-22 12:15:16

If

then

{7/3}
2013-05-22 12:01:08

No,i meant limit of f(g(x)) as x approaches a is equal to limit of f(y) as y approaches b.

bobbym
2013-05-22 05:42:52

Hi {7/3};

I probably am misunderstanding you but I am getting:

I am assuming f(x) is an arbitrary function since you did not specify one.





Let's say a = 1.



so b=2,





Which is a counterexample.

{7/3}
2013-05-21 19:08:40

My friend wants proof of this statement but i don't know how to prove it,can anyone help- If the limit of g(x) as x tends to a is b than the limit of f(g(x)) as x tends to a and the limit of f(y) as y tends to b is same

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