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What is function which is has irremovable discontinuity at x-2 removable discontinuity at x2 and continuous at other points?
Wiki User
∙ 9y ago
"Removable discontinuity" means the function is not defined at that point (it has a "hole"), but by changing the function definition at that single point, defining it to be certain value, it becomes continuous. "Irremovable discontinuity" means the function makes a sudden jump at that point. There are infinitely many functions like that; for example, you can set the function to be:
f(x) is undefined at x = -2
f(x) = 0 for x < 2 (except for x = -2)
f(x) = 1 for x > 2
Wiki User
∙ 9y ago
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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.
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.
What is the term for a function whose graph has no holes jumps or asymtopes?
continuous
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No. Not all functions are continuous. For example, the function f(x) = 1/x is undefined at x = 0.
What is the difference between continuous and uniformly continuous functions?
The way I understand it, a continuos function is said not to be "uniformly continuous" if for a given small difference in "x", the corresponding difference in the function value can be arbitrarily large. For more information, check the article "Uniform continuity" in the Wikipedia, especially the examples.
Is the greatest integer function a continuous funcion?
No. It has a discontinuity at every integer value.
Discontinuities of first and second kind?
A discontinuity of the first kind occurs when a function's limit does not exist at a specific point, while a discontinuity of the second kind happens when the function's value at a particular point is undefined or infinite. Discontinuities of the first kind can be classified as removable, jump, or infinite discontinuities, based on the behavior of the limit.
Which function has the following a vertical asymptote at x equals -4 horizontal asymptote at y equals 0 and a removable discontinuity at x equals 1?
2x-2/x^2+3x-4
How do you sketch a piece wise continuous function?
A piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:the domain itself is discontinuous (disjoint domains),the value of the function is not defined at the start or end-point of the domain ((a hole),the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).A piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:the domain itself is discontinuous (disjoint domains),the value of the function is not defined at the start or end-point of the domain ((a hole),the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).A piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:the domain itself is discontinuous (disjoint domains),the value of the function is not defined at the start or end-point of the domain ((a hole),the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).A piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:the domain itself is discontinuous (disjoint domains),the value of the function is not defined at the start or end-point of the domain ((a hole),the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).
Is a cosine function continuous?
Yes. The cosine function is continuous. The sine function is also continuous. The tangent function, however, is not continuous.
Does the cosine function appear to be continuous?
yes it is a continuous function.
Are there points of discontinuity for exponential functions?
There are no points of discontinuity for exponential functions since the domain of the general exponential function consists of all real values!
A polynomial function is always continuous?
Yes, a polynomial function is always continuous
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.
What function is continuous everywhere but not differentiable?
Weistrass function is continuous everywhere but not differentiable everywhere
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.
Is the infinite sum of continuous function continuous?
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
