MAT137Y1 Lecture Notes - Lecture 11: Classification Of Discontinuities, Inverse Trigonometric Functions, Algebraic Function
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A function f is continuous at x = c if lim f(x) = f(c). x c. A function f is left continuous at x = c if lim f (x) = f (c) x c- is right continuous at x=c if lim f(x)=f(c). x c+ A function f is continuous on an interval i if it is continuous at every point in the interior of i, right continuous at any closed left endpoint, and left continuous at any closed right endpoint. Constant, identity, and linear functions are continuous everywhere. In terms of limits, for every k, c, m, and b in r we have: k, c, m, and b in r we have: limk=k, limx=c, and lim(mx+b)=mc+b. x c x c x c. All algebraic functions are continuous on their domains. In particular, if x = c is in the domain of an algebraic function f , then we can calculate lim f (x) by evaluating f (c). x c.
