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Since your function is nonzero only at a finite or possibly countably infinite number of points, its integral will be zero.Jhenrique said:Hello!
We know how is a primitive of a any function (file 1), but how will be the graphic of a function like the at file 2 (is a descontinued function, periodic with a unit value in a point interval)?
?Jhenrique said:I found the answer for my question using the geogebra and ploting a simulation of an impulse function and then, integrating and deriving. I found that graphic will be so (file 3).
I don't think so, at least not on the basis of what you posted in file2. I think what you're talking about is the Dirac delta function (http://en.wikipedia.org/wiki/Dirac_delta_function).Jhenrique said:The ideia was that I wanted to know how plote o graphic of a primitive of a function like the file 2. But, how I'm autodidatic and pass the day studing math, I same already found the answer for my doubt (with much sacrifice, as always). The file 3 shows the primitives of a function (blue) with various impulses.
The delta function is sometimes thought of as an infinitely high, infinitely thin spike at the origin, with total area one under the spike, and physically represents an idealized point mass or point charge.
When I opened this topic, I don't was thinking in delta function, because I didn't understood how it works, so, I was trying to develop other way to arrive at same answer. Now I understood how the delta and heaviside functions works, but not perfectly, because I hoped to able to control the height of a pulse... How I can say if a pulse is bigger than other if all pulses are equal to ∞ ?? It's no make sense to me.Mark44 said:Your file2 graph seems to me to be three points. If you integrate that, you get zero. If you're talking about unit impulses, which are related to the Dirac delta function, you need to tell us that.
A point function is a mathematical function that maps each point in a given domain to a unique value in the range. It is typically represented graphically as a single point on a coordinate plane.
A point function is different from other types of functions because it only maps individual points to values, rather than entire intervals or ranges of values. It is also not defined by an equation or formula, but rather by a single point on a graph.
The graph of a point function is a single dot or point on a coordinate plane. It has no lines or curves connecting it to other points, as it only represents a single value at that specific point.
Point functions are commonly used in geometric and spatial analysis, such as mapping the location of objects or points on a map. They can also be used in physics and engineering to represent specific points in a system or model.
No, a point function can only have a single point on its graph. This is because it is defined by mapping each point in the domain to a unique value in the range. If there were multiple points, it would no longer be a point function.