There are 3 conditions that make a function continuous at a point.  Name the three conditions Give an example of a continuous function at a point, and work through the 3 conditions Give an example of a function that is discontinuous at a point. Specify which condition breaks down.

Q: Make a function that violates Clairault's Theorem. Explain why it does. Show how you got it.

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Q: Analyze the function f (x) -x + 18 if x 10

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Q: Graph each piecewise-defined function and find f(-5), f(-1), f(0) and f(3) [x-1,x<-1 S(x) =

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Q: Classify the following function. Determine the zeros, end behavior and intervals over which the…

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Q: I am required to determine whether or not each is a function. In addition, I have to provide the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Explain in many ways of why an absolute value Function an piecewise Function.

A: Given:   Explain in many ways of why an absolute value Function an piecewise Function.

Q: Briefly explain what the Mean Value Theorem tells us. Why do we require that f be a continuous…

A: Explanation given below...

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.