AP CALCULUS AB Section 1.3: Evaluating Limits Analytically PROBLEM OF THE DAY In the context of finding limits, discuss what is meant by two functions that agree at all but one point. Give an example of two functions that agree at all but one point. What is meant by an indeterminate form? In your own words, explain the squeeze theorem. EVALUATING LIMITS BY DIRECT SUBSTITUTION The easiest way to find a limit is by simply substituting the x-value into the given function. The problem with this method occurs when the x- value is not in the domain of the function or if the substitution results in an indeterminate form INDETERMINATE FORMS 0 0 00 0 0 1 LIMITS THAT FAIL TO EXIST Limits can fail to exist because of three major reasons Behavior that differs from right to left Unbounded behavior Oscillating behavior LIMITS THAT FAIL TO EXIST Behavior differs from left to right Unbounded behavior LIMITS THE FAIL TO EXIST Oscillation with limit Oscillation without limit DEFINITION OF CONTINUITY Informal Definition: a function is continuous if it has no breaks or holes over its domain Continuous Not Continuous WHAT DO YOU THINK?
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