AP CALCULUS BC by dffhrtcv3

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									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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