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It means that the function value doesn't make sudden jumps. For example, a function that rounds a number down to the closest integer is discontinuous for all integer values; for instance, when x changes from 0.99 to 1, or from 0.999999 to 1, or for any number arbitrarily close to 1 (but less than one) to one, the function value suddenly changes from 0 to 1. At other points, the function is continuous.
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Does the cosine function appear to be continuous?
yes it is a continuous function.
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.
What is the sin function?
It is a trigonometric function. It is also continuous.
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
Is a strictly monotonic function absolutely continuous?
No, they can only be jump continuous.
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.
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.
What is the sin function?
It is a trigonometric function. It is also continuous.
Are continuous functions integrable?
yes, every continuous function is integrable.
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
Is a strictly monotonic function absolutely continuous?
No, they can only be jump continuous.
What is a function whose graph has one or more breaks?
The tan [tangent] function.When a function has two or more brakes, this is not a continuous function, but it can be a continuous function in some intervals such as the tangent does.
