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Fyll_1_06analH_1

# Fyll_1_06analH_1 - FULLADIO 1 ANALUSH II SHMMU 2005-06...

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FULLADIO 1 ANALUSH II - SHMMU 2005-06 Sunart seic Poll¸n metablht¸n - Isostajmikèc - 'Oria 1. Na brejeÐ to pedÐo orismoÔ kˆje miac apì tic parakˆtw sunart seic: a ) f 1 ( x,y ) = ln(y 2 - 4x + 8) , b) f 2 (x , y) = p sin(x 2 + y 2 ) c) f 3 (x , y) = s x 2 + y 2 + 2x x 2 + y 2 - 2x 2. Na sqediˆsete ta qwrÐa tou epipèdou Oxy gia ta opoÐa h sunˆrthsh f ( x,y ) = y ( x - 1)( y - x ) eÐnai mh arnhtik . Sth sunèqeia na grˆyete tic isostajmikèc grammèc f ( x,y ) = c sth morf  y = g ( x,c ) kai na deÐxete ìti gia c = 1 / 27 den upˆrqei tm ma thc isostajmik c gramm c sth lwrÐda L = { ( x,y ) R 2 : - 1 3 < x < 1 } ektìc apì to memwnomèno shmeÐo ( 2 3 , 1 3 ) . 3. Na brejoÔn oi timèc thc sunˆrthshc f ( x,y ) = 1+ x + y sta shmeÐa thc parabol c me exÐswsh y = x 2 . Na parastajeÐ grafikˆ h sunˆrthsh g ( x ) = f ( x,x 2 ) . 4. Na brejoÔn, antÐstoiqa, oi isostajmikèc kampÔlec kai oi isostajmikèc epifˆneiec twn su- nart sewn: f 1 ( x,y ) = y x , b ) f 2 ( x,y ) = sin - 1

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Fyll_1_06analH_1 - FULLADIO 1 ANALUSH II SHMMU 2005-06...

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