Math 19: Calculus Winter 2008 Instructor: Jennifer KlokeLecture Outline (Introduction to Limits)Monday, January 14Theory: LimitsDefinition: In general, we say that the limit of the function f(x), as x goes to a, equalsL if we can make the values of f (x) arbitrarily close to L by taking x to be sufficiently closeto a but not equal to a. In this case, we write:limx→af(x) = L.If no such L exists then limx→af(x) does not exist.Intuitively, you can think of limx→af(x) as the quantity that outputs of f (x) are ap-proaching as inputs approach a.In other words, limx→af(x) is where it looks like the graph of f(x) is heading as x ap-proaches a.Examples: Limits from Graphs1. Consider the graph of f(x) below. What is limx→2f(x) ?2. Consider the following graph of g(x). What is limx→2g(x) ?13. Consider the following graph of h(x). What is limx→2h(x) ?Important lesson: the value of the limit limx→af(x) has nothing to do with the valuef(a).What to Know/MemorizeThe definition of the limit of a function f (x) as x →
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