EpsilonDelta

EpsilonDelta - Math 170 Kouba ‘ Precise Limits and...

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Unformatted text preview: Math 170 Kouba ‘ Precise Limits and Continuity for Functions of Two Variables DEFINITION : Let 2 = f(:c, y) be a function. The limit ( b) f(ac, y) = L means that $4] —) a, for each 6 > 0 there exist a 5 > 0 so that if 0<\/(:U—a)2+(y—b)2<5 , then |f(:1:,y)—L|<e. IT ['0 PH [N u r~ l m F-Ffifi-’flw—~— .- K9 1 Q\ \. \< X D DEFINITION : Function 2 = f(x, y) is continuous at point (a, b) ifI i.) f(a,b) is defined (finite) , ii.) lim f(:c,y) = L (finite) , (“Tim—Nam and iii.) lim f(w,y) = L . (mam—>011?) ------------------ ~-~~m~»:~-~ea<-~:713+%+x—H—++¥H4W~——~ ...
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This note was uploaded on 02/17/2012 for the course MATH 17C taught by Professor Lewis during the Summer '09 term at UC Davis.

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EpsilonDelta - Math 170 Kouba ‘ Precise Limits and...

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