Lesson 2-filled - Math 1314 Lesson 2 One-Sided Limits and...

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Math 1314 Lesson 2 One-Sided Limits and Continuity One-Sided Limits Sometimes we are only interested in the behavior of a function when we look from one side and not from the other. Example 1 : Consider the function x x x f = ) ( . Find ). ( lim 0 x f x Now suppose we are only interested in looking at the values of x that are bigger than 0. In this case, we are looking at a one-sided limit . We write ) ( lim 0 x f x + . This is called a right-hand limit, because we are looking at values on the right side of the target number. In this case,
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If we are interested in looking only at the values of x that are smaller than 0, then we would be finding the left-hand limit. The values of x that are smaller than 0 are to the left of 0 on the number line, hence the name. We write ) ( lim 0 x f x - . In this case, Our definition of a limit from the last lesson is consistent with this information. We say that L x f a x = ) ( lim , if and only if the function approaches the same value, L , from both the left side and the right side of the target number. This idea is formalized in this theorem:
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Lesson 2-filled - Math 1314 Lesson 2 One-Sided Limits and...

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