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lecture06

# lecture06 - Lecture 6 Ch14 Continuity Class 6 Continuity...

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2006 Fall MATH 100 Lecture 4 1 Lecture 6 Ch14 Continuity 00 (,) ( , ) Class 6 Continuity: Defintion: ( , ) is continuous at ( , ) if 1. ( , ) defined 2. lim ( , ) exists 3. lim ( , ) ( , ) xy x y fx y x y y y y y =

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2006 Fall MATH 100 Lecture 4 2 Lecture 6 Ch14 Continuity = + = + + = Otherwise y x z y x y x z y x y x y x z 1 0 , 0 0 ) 0 , 0 ( ) , ( 1 ) 0 , 0 ( ) , ( ) ln( ) ( : Examples 2 2 2 2 2 2
2006 Fall MATH 100 Lecture 4 3 Lecture 6 Ch14 Continuity )). , ( ( ) , ( is so , continuous are ) , ( & ) ( If (b) ). ( ) ( ) , ( is so , continuous are ) ( & ) ( If (a) : Theorem : function continuous of Compostion y x h g y x f h g y h x g y x f h g = =

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2006 Fall MATH 100 Lecture 4 4 Lecture 6 Ch14 Continuity 1 on except continuous 1 )) , ( ( ) , ( ) ( , 1 ) ( d) ( ) cos( ) , ( , ) ( ), cos( ) ( (c) 3 ) ( ) ( ) , ( , ) ( , 3 ) ( (b) ) ( cos( )) , ( ( ) , ( , ) , ( )), ( cos( ) ( (a) : Ex 2 3 5 2 5 2 3 3 = = = = = = = = = = = = = = = = xy xy y x y x h g y x f xy x h x x x g e y x f e x h z z g y x y h x g y x f x x h x x g y x h y x h g y x f y x y x h z h z g xy xy
2006 Fall MATH 100 Lecture 4 5 Lecture 6 Ch14 Continuity 0 ) 2 ( lim ) 2 ( lim ln lim ln lim ) ( ln ) ( lim , sin , cos : Sol ) ( ln ) ( lim : Ex : ity discontinu of point at Limit 2 0 r 1 1 0 r 1 2 0 r 2 2 0 r 2 2 2 2 (0,0) y) (x, 2 2 2 2 2 2 2 (0,0) y) (x, 3 2 = = = = = + + = + = = + +

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lecture06 - Lecture 6 Ch14 Continuity Class 6 Continuity...

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