01:640:135 Study Guide - Quiz Guide: River Irk, Trigonometric Functions, Binary Logarithm
17 Jan 2015
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Continuity: a function f is continuous at a point x=c if the following conditions are satisfied: f(c) is defined f ( x) f ( x)=f (c) lim x c lim x c. A function that fails to be continuous is said to have discontinuity at this point. Graphs to exemplify rules of continuity: f ( x) lim x c. = l f(c) does not exist f ( x)= lim x c. Does not exist becauseboth sidesa not equal f ( x)=l lim x c f(c) =k. K = l f ( x)= lim x c. Example: lim x c (x2 2 x 3) x 3 b) lim x c. Limit does not exist because it is not defined. Limit does exist because (x2 2 x 3) x 3 x = 3 lim x c if (x2 2 x 3) x 3. Example: f ( x)= { x + 2 if = f(x) < 1 x2 if = -1 x 1.
