Question: I need to come up with Calculus question that includes a function who has a function value at x that is different from the limit

I need to "come up with Calculus question that includes a function who has a function value at x that is different from the limit value at that same x. It's a good idea to look at piecewise functions and functions that have a hole in the graph. Does not exist is an acceptable limit or function value." But I am not sure where to start.

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