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# &aring;&macr;&frac14;&aelig;•&deg;&aring;’Œ&aring;&frac34;&reg;&aring;ˆ†

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± °ê ²n³ ¸ * ²n³ ¸ * ²n³ ¸ * ± PB Ê + ± & + ¸

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‚4²³“*± ± PB˚™+± 0 s t , 0 0 t s x , , 0 t t s , t t s v = 0 0 t t s s - - = ). ( 2 0 t t g + = , 0 0 0 t t 2 t) (t lim v 0 0 + = g t t s . 0 gt = 2 gt 2 1 s =
2. 0 ——

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, MN 0 M h MT, 0 MT μª C 0 M 0 0 . . 0 , 0 NMT MN ). , ( ), , ( 0 0 y x N y x M s s s MN 0 0 tan x x y y - - = ϕ , ) ( ) ( 0 0 x x x f x f - - = , , 0 x x M N C  → MT . ) ( ) ( lim tan 0 0 0 x x x f x f k x x - - = α = α ϕ→ 2 α ϕ T 0 x x o x y ) ( x f y = C N M x y
L²³…“*± : : 0 0 0 ) ( x x f y = ∧… ( , 0 x x x y x x , ) 0 + y x f x x f y - + = ); ( ) ( 0 0 x y x x x lim 0 0 2 2 2 2 2 2 2 , ) ( 0 x x f y = , ) ( 0 2 2 x x f y = , 0 x x y =

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. ) ( ) ( lim ) ( 0 0 0 0 h x f h x f x f h - + = : . ) ( ) ( lim ) ( 0 0 0 0 x x x f x f x f x x - - = x x f x x f x y y x x x x - + = = = ) ( ) ( lim lim 0 0 0 0 0 , ) ( 0 0 x x x x dx x df dx dy = = :
. , 0 0 0 0 x . ) ( , ) ( 0 0 0 0 0 0 0 I x f I x f y = H1²³“*±

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. ) ( , 2 2 x f I x x x f x x f y x - + = ) ( ) ( lim 0 0 . ) ( ) ( lim ) ( 0 h x f h x f x f h - + = : . ) ( ) ( . 1 0 0 x x x f x f = = . ) ( 2 x f . ) ( ), ( , dx x df dx dy x f y x x
2. 0 : 0 : 1. 0 : ; ) ( ) ( lim ) ( ) ( lim ) ( 0 0 0 0 0 0 0 0 x x f x x f x x x f x f x f x x x - + = - - = - - - ; ) ( ) ( lim ) ( ) ( lim ) ( 0 0 0 0 0 0 0 0 x x f x x f x x x f x f x f x x x - + = - - = + + + ) ( x f s 0 x s & & ) ( 0 x f - ) ( 0 x f + Ξ

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) ( x f s ( 29 b a , 0 0 & ) ( a f + ) ( b f - 2 ) ( x f s [ ] b a , 0 .
‚:²³“*± : : ); ( ) ( ) 1 ( x f x x f y - + = ; ) ( ) ( ) 2 ( x x f x x f x y - + = . lim ) 3 ( 0 x y y x = 1 . ) ( ) ( 0 0 0 C C x f = : h x f h x f x f h ) ( ) ( lim ) ( 0 - + = h C C h - = 0 lim . 0 = . 0 ) ( = C s

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& 2 . ) (sin ) (sin , sin ) ( 4 π = = x x x x x f s s s s : h x h x x h sin ) sin( lim ) (sin 0 - + = 2 2 sin ) 2 cos( lim 0 h h h x h + = . cos x = . cos ) (sin x x = 4 4 cos ) (sin π = π = = x x x x .
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## This note was uploaded on 09/28/2010 for the course MATH 210 taught by Professor Drzhao during the Spring '10 term at Kansas State University.

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&aring;&macr;&frac14;&aelig;•&deg;&aring;’Œ&aring;&frac34;&reg;&aring;ˆ†

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