Fyll03anal_07_1 - FULLADIO 3H - ANALUSH 2006-07...

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FULLADIO 3H - ANALUSH 2006-07 AKROTATA-PEPLEGMENES SUNARTHSEIS- ANAPTUGMA TAYLOR 1. Na brejoÔn ta akrìtata thc sunˆrthseic f ( x,y ) = R y x sin t t d t , x < y . 2. H jermokrasÐa se kˆje shmeÐo thc mpˆlac x 2 + y 2 + z 2 1 dÐnetai apì th sunˆrthsh f ( x,y,z ) = x - 2 y + 2 z . Na exetasteÐ an upˆrqoun phgèc jermìthtac sth mpˆla kai na brejeÐ h jermokrasÐa touc. 3. BiomhqanÐa qrhsimopoieÐ duo omˆdec ergazomènwn, teqnÐtec kai hlektrolì- gouc mhqanikoÔc diafìrwn eidikot twn. H sunˆrthsh f ( x,y ) = 64 x - 2 x 2 + 4 xy - 4 y 2 +32 y - 14 , ìpou x o arijmìc teqnit¸n kai y arijmìc hlektrolìgwn mhqanik¸n, ekfrˆzei tic monˆdec tou paragìmenou proðìntoc anˆ ¸ra. i) Poièc timèc twn x,y megistopoioÔn thn f ? ii) An diˆforoi lìgoi epibˆlloun ton periorismì x + y 54 na brejoÔn oi timèc twn x,y pou megistopoioÔn thn f . 4. Na melet sete ta akrìtata thc sunˆrthshc z = z ( x,y ) pou orÐzetai upì peplegmènh morf  sto parˆdeigma 4.4, selÐda 202 tou biblÐou. 5.
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