lecture07

# lecture07 - Lecture 7 Ch14 Differentiability Class 7...

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2006 Fall MATH 100 Lecture 4 1 Lecture 7 Ch14 Differentiability ) ( ' define and ) ( ) ( let we , definition e alternativ an make To exists. ) ( ) ( lim ) ( ' i.e., , at derivative has it if at able differenti said is variable one of function A : ability Differenti 7. Class 0 0 0 0 0 0 0 0 0 x f x f x f x x f f x x f x x f x f x x x Δ Δ = Δ + = Δ Δ Δ + = Δ ε

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2006 Fall MATH 100 Lecture 4 2 Lecture 7 Ch14 Differentiability 0 where ) ( ' form in the written be can such that ) ( ' number a exists there if at able differenti be to said is : Definition ) ( ' Then 0 0 0 0 ⎯→ Δ + Δ = Δ Δ Δ + Δ = Δ Δ x x x x f f f x f x f(x) x x x f f ε
2006 Fall MATH 100 Lecture 4 3 Lecture 7 Ch14 Differentiability 0 lim 0 ) ( ' lim lim ) ( ' : ion Justificat 0 0 0 0 0 = = Δ Δ Δ Δ = Δ Δ Δ ε x x x x f x f x f x f

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2006 Fall MATH 100 Lecture 4 4 Lecture 7 Ch14 Differentiability 0 ) , ( as 0 ) , ( 0 ) , ( where ) , ( ) , ( and exist ) , ( ) , ( if ) , ( at able differenti be to said is : Definition ) , ( ) , ( Define : space - 2 in ability Differenti 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Δ Δ Δ Δ Δ Δ Δ + Δ + Δ + Δ = Δ Δ + Δ + = Δ y x y x y x y x y y x f x y x f f y x f y x f y x f y x f y y x x f f y x y x ε εε
2006 Fall MATH 100 Lecture 4 5 Lecture 7 Ch14 Differentiability 0 ) , ( as 0 2 ) , ( 0 ) , ( since

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lecture07 - Lecture 7 Ch14 Differentiability Class 7...

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