One- and Two-Sided Limits When we write we mean the number that (x) approaches as approaches 2 We examine values of f x from both sides. f (x) as approaches 2 through values greater than 2 (such as 2.1, 2.01, 2.003) and values less than 2 x (such as 1.9, 1.99, 1.994). If we want to approach 2 only through values greater than 2, we write x for the number that (x) approaches (assuming such a number exists). Similarly, f denotes the number (if it exists) obtained by letting approach 2 through values less than 2. We call a x and a Problems and ask for formal definitions of left and right-hand right-hand limit left-hand limit. limits. For the function graphed in Figure , we have
One- and Two-Sided Limits When we write we mean the number that f (x) approaches as x approaches 2 from both sides. We examine values of f (x) as x approaches 2 through values greater than 2 (such as 2.1, 2.01, 2.003) and values less than 2 (such as 1.9, 1.99, 1.994). If we want x to approach 2 only through values greater than 2, we write for the number that f (x) approaches (assuming such a number exists). Similarly, denotes the number (if it exists) obtained by letting x approach 2 through values less than 2. We call a right-hand limit and a left-hand limit. Problems and ask for formal definitions of left and right-hand limits. For the function graphed in Figure , we have