2.2 The Limit of a Function [Part 2) The Existence of a Limit For a limit to exist at a point, the functional values must approach a single real number at that point. 1. Evaluate lim sin (3) using the graph of sin (1). x x>O x Note: The graph of sin G) oscillates rapidly between -1 and 1 as x approaches 0. 2. We could create a table of values to evaluate lim sin (1). Let's take a more systematic approach. The following sequence ofx _values approach 0: x>0 X x 2 2 2 2 2 2 1: 311 511 71r 91': 111T . (1 1 Und. sm x One-Sided Limits: Right-Hand Limit Suppose f (x) is defined for all x near a with x > a. If the values of the function f (x) approach the real number L as the values of x approach a (x > a), we write lim f(x) = L x-at and say the limit of f (x) as x approaches a from the right equals L. Left-Hand Limit Suppose f (x) is defined for all x near a with x 2 a. lim f (x) = X - 2 - b. lim f (x) =_ x- 2+