ma1012_hw14_201012

B d c 5 c dx b x bxy y cy csc 2y c35y 2x 2 cb xyb y

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Unformatted text preview: x$Êc cyœw7x 2(xy)b cot4ˆ& t ‰‰ 2) † dcˆ" bb cot ˆ‘t ‰‰# œ c2 ˆ1 b cot ˆ t ‰‰c$ †yˆccsc# ˆ t x ‰ † d ˆ t ‰ b" 6] œ c6y(3xy b 7) 42. y œœ 1 b & b 7) c Ê # < dx dx x ˆ ˆ d" & 26. ydx dy sin xc x cos 1 Êy c c x 1d asinc #xb b sin x x1 ††csc (xy) ‰ cc3y d ab $ ˆxb c cos$ x † d ˆ x ‰ # ‰ dt # œ " x(3xy ˆ c x 3x y œ " x dx ˆ x Œ x cos Step 4: "#x "c" c2xy" y# 3 È "‰cdt †ˆc c" ˆ dxy b y ‰ˆc$x " ‰ " dt c" ˆˆc 3 yÈ# ‰‰c$ x<dx9" yc"Î# x ‰# È ‰ dx ‘3 œ ˆxc$Î# ˆ # ‰È t ‰ 2xy x y dr 19. " acyw (0) cagain, (0)œ a2bc& tangent ‰ c xœ“sin 2x x the c x) c cos$ x 3 ˆ È 1c œ dx # s b ' 2 c xˆ ‰ secx b tan " to‹ 3 a3‹# x 1 sin x c# x w ‰ sin 2x) Ê Šsec Ècosˆ2x # ’csc5ˆx in)œ‰x1cosywwbxb ŠsinÊ 3x) ˆc È)xyŠ aÈœ cos#at b (coriginbis yaœ 2x; b ˆ " ‰ 1 c x b 1 ‰c Ê d œ y œ 2 )‹Differentiating b tan ) œ secÊ œ œx ) œ dy xx x 3# ) 3 (x b 1) c (x c 1) ˆ t "‰ ‰ ˆ dy c" c y sec (xy) # œ (x 2 29. Êcos1ˆ x) y(x 'œ w c$ "Î$ c " cos#&(xy)c y y " tangent y $ sec# ˆ dy x c b cot"c sec#Î$ Ê c b "Î$0 c%Î$ Š cos x dy ‹ œ" cos sec ) " sec ˆ x tanÊ) œ bc"Î%Ê)bd"tan1‰inÊc1))!(tan xb1b""csincÈx tand ˆ œ b#xˆdx ˆ xÈ0toÊ œ3csin(xy) at the c1 c yis ‰ c"Î$ yw œ ctanœbdxy5œ(xy)b xy‰(0) )œ sec")) sec "x)œ 1 x " Êsec c‰ cx" c$ x xc " x ‰ dx œ origin sec (xy) Ê dx œ x sec (xy) c b csin 1) " (sec"Î# b# ) ) b $ 1) 25.tan ))x#È3 x (sec y bŠc)#)x dy y ‰ sœ sin ˆœ c Èxcos tan È3 tan # bb ‹ # 3xdy b 3y x #‰ Š # dyÈ #‹ c(x) b œc Ê 3y " (sec È x #) ) ‰ b b t20.ˆ " ‰ b y$ b ) dx ) sec )# œ #tan Ê 3xsec È)#‹#” œ 18y b 18x #x 1 a• 3 c 18xb # œ 18y c 3x# Ê dy œ 6y c x ˆ ) " È an ) x x x 18xy ) œ Š b 3y dx dx y dx y c 6x y c ) c # x.# The tangents are perpendicular to each other at È) ccos (xy) c ) the d product ofdx their slopes is œ sec 1(xy) c y œ ccos (xy) c x# the origin since œ d x 43. y .œx sin acos (2t c 5)b x # dy c" cos (cosx #c 5)) † dt cos w(2t cc 3x œ 2xy (cos (2t c 5))c#(csin (2t c 5)) † dt (2t c 5) Ê dt œ w (2t 5) c cos † 29b x#"yw œ 1 c yw Ê ax b 1b y œ 1dy 3x7 c 2xy Ê yd œ 1 ( # 1 .œ x c y Ê 3x r b 2xy œ " r (3x c 2) b ˆ4 c w " ‰ " Ê # cœ (3x c 2)' " (3x c 2) 1b (c1) ˆ4 cˆ "(x‰ ‰ Š x yd ‹ˆ4 c " ‰ d cos dr 27. y 51. ) # œ # , y: c csc cb xc 21 #x s (r)) Ê d)21. wc cos (r)))y#œcx)cot2x Ê(2t cw 5))(sinb 29c 5))dxÈ c ‰1)(3) œb 1 ; then yww x cy1) (xÊ1)y wwœ y cx 3 1) † dx(3x c 1) † dx csc (3x c 1)) œ 39.(r yyœ 21 cos (cos 1) Ê y #œ (2t csc d (3x 2x b 2 œ x c † dx # (3x b cx b y œ # 2 (csc w 2 (3x œ c œc dq (mx) # t y 2xy bcos œx bÊ cw (0)2yy œ 2x0 b 1 (1)ʆ dt # œ b 12y x ‰ Ê y3 œ c " dy d y y sin† d ax Êb x)‹d†mcoscbx...
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