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Continuity - Concept

Teacher/Instructor Norm Prokup
Norm Prokup

Cornell University
PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

In order for a function to be continuous at a certain point, three conditions must be met: (1) that the point is in the domain of the function, (2) that the two-sided limit of the function as it approaches the point does in fact exist and (3) the value of the function equals the limit that it approaches. The continuity of a function only exists if these three conditions are met.

I want to talk about a concept called "Continuity," let f of x be a function here is the definition of Continuity.
We say that f of x is continuous at the point x=a if three things are true. First f of a is defined so a has to be in the domain of the function f. Second the limit as x approaches a f of x exists, so the limit has to exist from both sides. And then three the limit as x approaches a of f of x has to equal f of a. So this value in part one has to equal the value in part two. These are the three conditions for Continuity of a function at a point x=a.

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