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What function is integrable but not continuous?
A function may have a finite number of discontinuities and still be integrable according to Riemann (i.e., the Riemann integral exists); it may even have a countable infinite number of discontinuities and still be integrable according to Lebesgue. Any function with a finite amount of discontinuities (that satisfies other requirements, such as being bounded) can serve as an example; an example of a specific function would be the function defined as: f(x) = 1, for x < 10 f(x) = 2, otherwise
Is a corner continuous?
Yes, a corner is continuous, as long as you don't have to lift your pencil up then it is a continuous function. Continuous functions just have no breaks, gaps, or holes.
What is the important similarity between the uniform and normal probability distribution?
They are both continuous, symmetric distribution functions.
What are some similarities and differences between quartic and cubic functions?
The similarities are that they are polynomial functions and therefore continuous and differentiable.A real cubic will has an odd number of roots (and so must have a solution), a quartic has an even number of roots and so may have no solutions.
Is a continuous decimal a rational number?
There is no such thing as a continuous decimal.
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.
Do all functions have integrals?
No, all functions are not Riemann integrable
What are the criteria for determining acceptable wave functions in quantum mechanics?
In quantum mechanics, acceptable wave functions must be continuous, single-valued, and square-integrable. They must also satisfy the Schrdinger equation and have finite energy.
Let f be an odd function with antiderivative F. Prove that F is an even function. Note we do not assume that f is continuous or even integrable.?
An antiderivative, F, is normally defined as the indefinite integral of a function f. F is differentiable and its derivative is f.If you do not assume that f is continuous or even integrable, then your definition of antiderivative is required.
What has the author Krzysztof Ciesielski written?
Krzysztof Ciesielski has written: 'I-density continuous functions' -- subject(s): Baire classes, Continuous Functions, Functions, Continuous, Semigroups
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
What function is integrable but not continuous?
A function may have a finite number of discontinuities and still be integrable according to Riemann (i.e., the Riemann integral exists); it may even have a countable infinite number of discontinuities and still be integrable according to Lebesgue. Any function with a finite amount of discontinuities (that satisfies other requirements, such as being bounded) can serve as an example; an example of a specific function would be the function defined as: f(x) = 1, for x < 10 f(x) = 2, otherwise
Are all functions continuous?
No. Not all functions are continuous. For example, the function f(x) = 1/x is undefined at x = 0.
Are all polynomial funcions continuous?
Yes, all polynomial functions are continuous.
Can all functions be discrete or continuous?
No. There are many common functions which are not discrete but the are not continuous everywhere. For example, 1/x is not continuous at x = 0 (it is not even defined there. Then there are curves with step jumps.
What has the author Jean Schmets written?
Jean Schmets has written: 'Spaces of vector-valued continuous functions' -- subject(s): Continuous Functions, Locally convex spaces, Vector valued functions
What is a spectral curve?
A spectral curve is a mathematical concept used in the study of integrable systems, particularly in the field of integrable models in mathematical physics. It is a curve in the complex plane associated with a particular integrable system, providing information about the system's eigenvalues and other important properties. Spectral curves play a key role in understanding the dynamics and properties of integrable systems.
