CAS MA 123 Lecture 6: Important End Behavior
27 Sep 2015
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Continuity: f(x) is continuous at x=a if lim x a f(x) = f(a) 3. f(a) is defined lim x a f(x) must exist lim x -a f(x)= lim x +a f(x) the numbers in 1 and 2 are equal. Example #1: x2+1 x 2 x is not defined at x=2 therefore the function is not continuous f(x) = If p(x) is a polynomial, then p(x) is continuous at every point x=a > lim x a p(x) = p(a: f g composition; this can also be written as f g(x) = f(g(x), ex #1. F(x) is continuous on (- , 2] and is also continuous on (2, ) a. b. f(x) is discontinuous at 2. It is the lower portion that is continuous because the limit equals the value of the function. I = (b, c) or [b, c) or (b, c] or [b, c]
