Sec12.2 - Sec.12.2 Limits and Continuity in Higher...

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Sec.12.2 Limits and Continuity in Higher Dimensions Let f be a function of two variables whose domain D includes points arbitrarily close to (a, b) . The limit of f(x, y) as (x, y) approaches (a, b) is L and we write (,) (,) lim ( , ) xy ab f xy L if for every number >0 there is a corresponding number >0 such that (, ) fxy L whenever (x, y) is in D and  22 0 xa yb  . Note that (x, y) may approach (a, b) in infinitely many directions and paths as long as (x, y) is in D. Look over limit rules on page 712 of our text. If any two of the ways that (x, y) approaches (a, b) do not yield the same limit, then we say the limit does not exist. EX1 Find the following limits. A. (,) ( 1 , 2 ) 32 lim x y B. 0 , 0 ) lim x y x y Note: L’Hospital’s Rule doesn’t apply because we have more than one variable. C. 0 , 0 ) cos lim 3 x y x y
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This note was uploaded on 02/03/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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Sec12.2 - Sec.12.2 Limits and Continuity in Higher...

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