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Does every continious function has laplace transform?
There are continuous functions, for example f(t) = e^{t^2}, for which the integral defining the Laplace transform does not converge for any value of the Laplace variable s. So you could say that this continuous function does not have a Laplace transform.
Every continuous function is integrible but converse is not true every integrable function is not continuous?
That's true. If a function is continuous, it's (Riemman) integrable, but the converse is not true.
Are continuous functions integrable?
yes, every continuous function is integrable.
Is every continuous function is bounded in C?
No. y = 1/x is continuous but unbounded.
What is the difference between a continuous signal and a discrete signal?
A continuous signal is one that is measured over a time axis and has a value defined at every instance. The real world is continuous (ie. analog). A discrete signal is one that is defined at integers, and thus is undefined in between samples (digital is an example of a discrete signal, but discrete does not have to imply digital). Instead of a time axis, a discrete signal is gathered over a sampling axis. Discrete signals are usually denoted by x[k] or x[n], a continuous signal is x(t) for example. Laplace transforms are used for continuous analysis, Z-transforms are used for discrete analysis. Fourier transforms can be used for either.
When finding the derivative of a point on a piecewise function does every function in the piecewise function need to be continuous and approach the same limit?
All differentiable functions need be continuous at least.
Can a function have a limit at every x-value in its domain?
Yes, that happens with any continuous function. The limit is equal to the function value in this case.Yes, that happens with any continuous function. The limit is equal to the function value in this case.Yes, that happens with any continuous function. The limit is equal to the function value in this case.Yes, that happens with any continuous function. The limit is equal to the function value in this case.
How do I show that a given function f is continuous everywhere?
Υou show that it is continuous in every element of it's domain.
Is the greatest integer function a continuous funcion?
No. It has a discontinuity at every integer value.
Does Naruto get an extra tail every time he transforms?
No
What is the definition of a continuous function?
Intuitively, a continuous function y = f(x) is one where small changes in x result in small changes in y. More rigorously, consider the function y = f(x) defined on the domain D to the codomain C where both D and C are subsets of R. Then f(x) is continuous at a point p in D if the limit of f(x) as x approaches p within D is f(p). The function is said to be continuous is it is continuous at every point in its domain. The domain and codomain of f can be extended to multiple dimensions provided a suitable metric (eg Pythagorean distance) is used.
What is the function of prism?
It transforms incident rays (say, from the Sun) of white light [that contains almost every light frequency] into, by Refraction, a Rainbow. Please ask next - What are the main Astronomical uses of the Prism.
