Re: lim f(x)/x

On 30-09-2005 16:59, stat wrote:

Thanks for responding to my post...
N is an integer...
x , xo are real numbers...e (as in epsilon) and delta are real numbers arbitrarily small.
I'm sure you are familiar with the epsilon ,delta usage in the definition of continuity in most standard texts of Calculus... 

I sure am. But you cannot just say that "x , xo are real numbers" and so
on. Are you saying, for instance, that what you wrote is true for
*every* real number _x_? Or are you saying that it's true for *some*
real number _x_. The same questions apply to _xo_ (BTW x0 or x_0 are
better choices) and to all the other numbers that you've mentioned.

As for the nondecreasing part I think that maybe is not necessary but if I don't use it I probably have to use
absolute values in the inequality...
instead of 0<=f(x)-f(xo) <= e*(x-xo) use 0<=| f(x) - f(xo) | <= e* | x-xo |
But the question remains is my "proof" a proper proof or just nonsense? 

It will be hard for me to answer that until you tell me more about all
those numbers. And another thing: why did you write that 0 < f(x)/x?

Best regards,

Jose Carlos Santos
.

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