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Is the value of a function defined as the limit as x approaches each value in the domain of f(x)?

What happens if at a specific x, you have f(x)-> 0/0? is there usually a limit for which f(x) approaches in this situation?

What happens if at a specific x, you have f(x)-> 0/0? is there usually a limit for which f(x) approaches in this situation?

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