lecture25

# lecture25 - MATH 100 Lecture 25 Final review Class 25 Final...

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2006 Fall MATH 100 Lecture 8 1 MATH 100 Lecture 25 Final review ( 29 44.)) 33, 15.2 (Ex ) , ( ) , ( lim Continuity b. exist t doesn' ln lim ) , ( lim limits a. 0 0 ) , ( ) , ( 2 2 ) , ( ) , ( ) , ( ) , ( 0 0 0 0 0 0 y x f y x f y x xy L y x f y x y x y x y x y x y x = + = Class 25 Final review 1.Function of two or more variables

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2006 Fall MATH 100 Lecture 8 2 MATH 100 Lecture 25 Final review ( 29 29) 11, 15.5 (Ex 0 ) ) ) 0 ) , ( ) , , ( for 0 ) ) ) 0 0 of plant Tangent d. 40) 15.3 (Ex . ' 0 ' 2 2 1 ation differenti implicit & function defined Implicitly c. 0 0 0 0 0 0 0 0 0 0 2 2 = - + - + - = - = = - + - + - = - = - = = + = + z (z y (y f x (x f z y x f z y x g z (z g y (y g x (x g x x ) ,z ,y g(x g(x,y,z) y x y yy x y x y x z y x
2006 Fall MATH 100 Lecture 8 3 MATH 100 Lecture 25 Final review z y x y x g g g g y x y x y f x f y x f , , f.Gradient 45) 15.4 (Ex . 0 & as 0, , ) , ( al differenti Total e. 1 2 1 2 1 = + + + = ε ε ε ε ε

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2006 Fall MATH 100 Lecture 8 4 MATH 100 Lecture 25 Final review D>0 Real min Real max D<0 Saddle saddle D=0 ? ? test partial Second ) , ( 0 0 ) , ( ima, maxima/min local int Unconstra h. 19) 15.7 Ex 30, 15.6 (Ex 1 , s derivative l Directiona g.
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