A function is continuous when its graph is a single unbroken curve ... that you could draw without lifting your pen from the paper.

A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can …

A function f (x) is said to be a continuous function at a point x = a if the curve of the function does NOT break at the point x = a. Learn more about the continuity of a function along with graphs, …

Nov 16, 2022 · From this example we can get a quick “working” definition of continuity. A function is continuous on an interval if we can draw the graph from start to finish without ever once …

In calculus, a continuous function is a real-valued function whose graph does not have any breaks or holes. Continuity lays the foundational groundwork for the intermediate value theorem and …

In this section we will examine what it means graphically for a function to be continuous (or not continuous), state some properties of continuous functions, and look at a few applications of …

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Nov 22, 2025 · Formally, a function f (x) is continuous at a point x = a if three conditions hold: f (a) is defined (the function has a value at a). lim⁡x→a f (x) exists (the limit from both sides …

In this section we introduce the idea of a continuous function. Many of the results in calculus require that the functions be continuous, so having a strong understanding of continuous …

In Continuity, we defined the continuity of a function of one variable and saw how it relied on the limit of a function of one variable. In particular, three conditions are necessary for f (x) to be …