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# Continuity - Concept

FREE###### 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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###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

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