SurCalNotesCh2Sec1and2 - Survey of Calculus 2.1 Fall 2002...

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Survey of Calculus Fall 2002 Smith 1 2.1 Limits and Continuity Limits There are basically three ways to evaluate limits: (1) _____________________ (2) _____________________ (3) _____________________ I. Evaluating limits graphically . A. The limit of f(x) as x approaches a certain number, c, is the ____________________ that the function gets “___________________” (i.e., the y-value “gets closer to”) as x gets “close to” c (from both sides). Note: The limit of function is NOT the same as the functional value! Example: Consider the graph of 3 3 2 ) ( 2 = x x x x f . (You will need to put the hole in the graph. I can’t get my computer to do it for us. Do you remember where it belongs from College Algebra?) x y -4 -3 -2 -1 0 1 2 3 4 0 1 2 3 4 5 Notice that as x gets “closer to” 3 from both sides, the y-value gets “closer to” ___________. This means that the limit of f(x) as x approaches 3 is ______________. B. Notation: is read as “the limit of f(x) as x approaches c equals L”. In the example above, L x f c x = ) ( lim ) ( lim 3 x f x = ____________. C. If the limit of a function exists, it must be a single real number. Otherwise, we say that the limit ______________________________(DNE). We may use the symbols _____ and ________ to indicate that the values of a function become arbitrarily large or arbitrarily small. Note the paragraph on p. 89.
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Survey of Calculus Fall 2002 Smith 2 One –Sided Limits A. means the y-value that function gets “close to” as x gets “close to” c from the ______________. ) ( lim x f c x B. means the y-value that the function gets “close to” as x gets “close to” c from the _____________.
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This note was uploaded on 01/12/2012 for the course MATH 2043 taught by Professor Pamelasatterfield during the Fall '05 term at NorthWest Arkansas Community College.

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SurCalNotesCh2Sec1and2 - Survey of Calculus 2.1 Fall 2002...

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