The limit of a function exists if and only if the left-hand limit is equal to the right-hand limit. lim x → a − 1 f ( x) = lim x → a + f ( x) = L Note: The limit of this function exists between any two consecutive integers. Properties of Limits If

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But the example you give is not a function inside a function- you have a linear combination of two functions. One of the very first laws of limits you should have learned is