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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
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Are continuous functions integrable?
yes, every continuous function is integrable.
A polynomial function is always continuous?
Yes, a polynomial function is always continuous
What function is continuous everywhere but not differentiable?
Weistrass function is continuous everywhere but not differentiable everywhere
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.
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.
