ma1012_hw14_201012

2tdy y dy y 0 33 63 cos c x dx yc5xdyc

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Unformatted text preview: 9 2‹ ycosy #'ŠÊ td 1(x) † Èt œ m; ty cy b"x‰ dy mÊd (cosw' c x)m cos ˆy#c 1 Ê dy œ yy c 1 œ30.35. #t 7sin œ cos x † œ m‹ (cos y) dy" œyˆ ˆt sin ˆ (mx) œ xy cos ˆ % œ cos Š " œ m‰ bdy yc ‰ Section 3.6 Implicitdx csc (3x c 1) dx ndt x dx b t b 1 dx a Šœ tcb(bdyc 2) cÈtdx cc1)(3x cˆdxxt b 1‰ (3x cœ (3x c 2) c 1)) œ Differentiation (3x163x È dt xÈ b 1 3x (3x † 3 b1(csc 4 b y 1) 1)( " 1) 1) 2 cot coscc 21y # " " S (0)# œc d 2x cscww 2yy‹c 3 b 1) 1 Èdycot x dx † dx (3x " # yw (0) œ c dy cos tep 1:84 Š#.3 œChapterb 2y‰ dx œ 1, b dx x Š4 c ‹ y b m (x Differentiation ybd dy x dx y ‰ œ sec44.xÊ.œ ySinceœ ˆ ‰ Ê dy œ the ˆ5 sin t ‰‰ d 5 sin ˆ t ‰‰ œ at the origin. m m † c 2dxtt Êx)dx b coscty œ ycos cos dx5t sin ˆ†t ‰c tm 2 œ c csintangentˆlines† areˆperpendicularcsin ˆ5 sin ˆ t ‰‰ ˆ5 cos ˆ t ‰‰ † d ˆ t ‰ 1 dx (cos ˆ 39 2(t b 1) c 1 t b dt 3 3 3 dt 3 ‹ ‹ Ê c w œ tm ‹ Š 2(t 5 xx " œ 3Š t value‹ cos Š and "dy 3 is #dt y cos tsin x)b $ œ cos Š 2x cos (mx).1) The largest b¹ b1 b dr dy œ 2y c(mx)bb csc2 xÈ31.1 ÊœcŠtaninœc1sin xy wdyœˆ9y ’cos(mx)‰can‰attainsec1“at ‰sin Š yÊœthe†œ cx ˆ value Êx ‰ tan ˆ x ‰‰ ˆ " ‰ œ 2 sec# ˆ x ‰ tan ˆ x ‰ sin œ r œ c# ) Ê yœœ b ‹ˆ b5y c ˆ2(t‰Ê cos œ 3 ˆ x"Èt † 1dx ¹ " † dy 1 x x œ 0 ‹ † dy largest x c y ˆ...
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