Describe the difference between a discontinuity that is removable and a discontinuity that is nonremovable. Then give an example of a function that satisfies each description. (a) A function with a nonremovable discontinuity at x = 4 (b) A function with a removable discontinuity at x = −4 (c) A function that has both of the characteristics described in parts (a) and (b)

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A: We can use the concept of calculus and function in order to solve the given question.

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Q: 3) Without a graph, how can one show differentiability of a function at apoint?

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Q: When is a function said to have the Intermediate Value Property?

A: Let f(x) be any  function which is continuous and defined in the interval [a, b].

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A: Question : Right most x value where f(x)=3

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A: Given function  f(x)=-48x-3

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Q: Explain Limits for Functions of Two Variables?

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Q: This describe the value of a function as approaches to some value?

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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.