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What is function which is has irremovable discontinuity at x-2 removable discontinuity at x2 and continuous at other points?
"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
What else can I help you with?
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
Are all functions continuous?
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
What is discontinuity?
A continuous spectrum contains all the wavelengths. A discontinuous spectrum has stripes of specific colors and can be used to identify the elements making it
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.
What is a discontinuity?
It's when a Basketball player dribbles the ball, stops briefly, and then resumes dribbling.
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!
Does the cosine function appear to be continuous?
yes it is a continuous function.
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
