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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.
Is a strictly monotonic function absolutely continuous?
No, they can only be jump continuous.
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
