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Give an example of the following or explain why no such example can exist. Make sure you explain why your examples satisfy the properties. (a)

Give an example of the following or explain why no such example can exist. Make sure you explain why your examples satisfy the properties.

(a) A function f (x) such that f (x) < 0 for all x, but f (x) > 0 for all x.

(c) A function f (x) such that f (99)(x) is not the zero function1, but such that f (100)(x) is the zero function.

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