. . . . .Not sure what you mean by a limit function.
A limit, in mathematics, embodies the idea of a sequence of some sort
getting ever closer to some fixed quantities.
So if the sequence is of numbers then if each term get closer and closer
to some number then we say it approaches a limit
eg the sequence
{1/1, 1/2, 1/3, 1/4, 1/5......}
get closer and closer to zero the further along the sequence we go.
To have a limit function we would have to have a sequence of functions
that became closer and closer to the particular series, the further we
went along the sequence.
Fourier series provide and example of this, the more terms we employ
the closer the Fourier series matches the function we are approximating.
Taylor / Maclaurin series are another example of this.
You will have to tell us more about the context if you want greater detail.
The physical borders for mathematical limits can beThey can be.
Speed of light for matter is a limit function,
you can get as close as you have energy for but never hit it.
Fundamentally it is a basic calculus concept.
1)You do realize that made absolutely no sense?
An electron is a form of matter, it has mass, there is bound by many
of the properties of matter. We still use electrons in ballistic forms
in many uses, tubes (aka valves), sputtering chambers,
ionization of gases, etc.
OK. I will try to say my opinion in other way.You are getting off topic for this thread.
Pick it up in your own threads.
No I don't agree.So in mathematics, a limit is a value of a function when one or more of that functions parameters approaches some set value from both sides.
No I don't agree.
For instance consider the function
\(\left\{ y(x) = {x^2},\,x \not= 0 \\
y(x) = 1,\,x = 0 \\
\right\}\)
The limit as the function approaches zero from both plus and minus is zero, but this does not equal the value of the function, since
\(\lim_{x \to 0 - } = 0 = \lim_{x \to 0 + } \)
What you have stated is the condition for the function to be continuous at a point (in this case the point zero).
That is a function is continuous at a point if the value of that function equals the limits when approached from + and from minus.
So my example function is not continuous at zero, nor is it differentiable at this point.
It is both at every other point, however.
I'm sorry I don't understand this response at all.and stated that the limit appears to be 0 if we look at the left and right side limits, but it's 1 for x=0 so 0 cant be the limit.
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