For each of the following, you may either give an explicit formula for a func- tion, draw a picture of a function, or say why such a function does not exist. (a) A function that is continuous at a point x = a but is not differentiable at x = a. (b) A function that has a critical number x = a but no local extrema at x = a. (c) A function that has a limit at x = a but is not continuous at x = a.

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A:

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A: We have to solve by given data

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A: We can find where the function is discontinuous.

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A: Given query is to to find which is larger from the graph.

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A: The complete solutions are given below

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A:

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.