ma1012_hw14_201012

Cos1 x yx w c c cosxyc y y tangent y sec

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Unformatted text preview: 6 d 1 bd" ‰ c# b 1d b " ‰x an ˆ ˆ4b ‰ sec œ sin 37.sec œ cy b3 tanœˆ1 2x b42yy ˆœ ‰ dy 2yy‰d‘œ c2x Ê dy œ yw œ c ˆ; now to find# ˆ y , ayw b œ d c (2x c ˆ œ w (x 1 c y(x 4 y) x4 x .œ x sin x b x ‰c y c x ‰ 0 Êx Ê 25.45bˆc œ 1ˆ2 b x cosx #c x Êy dx œ x1 ˆ1 bsin xb b sin x † dx axx# byb x xd acos x xb bdxx ˆ x x † dx Š x y ‹ x cos (x) a "x œ x # 1 x tbc xy 1 31t #19. x31t b xy# œ 6:# 31t Ê 3dy œ (2 1t dy t) † d dy dx1t) 1 (2 sec dx t)(sec 1t tan 1t) †dx (1t) œdx 1 sec# 1 t tandx t " ‰ d ˆ # y‰ 1 40. y 1 tan 1 t" 1 dt sin sec 1 sec (sec 1 yœ ˆ ‰ sec # c sin b cos t †ˆdt ‰ œ27.œx32œ6# ˆ1ˆb Ê c1œ a2 ‰ ˆ#3yb‰dx y(1) dtdx 2œ sec y ‰œ cosand ydw (1) œ 1 ‰Ê tangent line2is œ1 # sec 1 # 1 Ê œxcos4y # x ‰ ˆ d 2(sin 2; ‰ b 2x Ê % x b x ˆˆ 42 cos2 $ x † (cos x) b cosdt # x $ c œ slope of tangent iscybthus, ‹ sin œ tan c œ c y b x x) x Šc x # 4 œ x ˆ sin 1)x by x=1 d "Î# ‰ dx y Èx‰ b 7 Ê Sw (x) 49. 2dxxˆtan ˆ2xbxy2x‹ b Š ˆ2x"Î#dy b cos b 0 (cos (7t) sin (7t)) ˆ2dy œ 3 c1 b cos#tep 1:# x ycos (7t)(csin (7t))(7)xœ 2y7s‰1†bdy(x)#1(7t)xd#0 d y œ yww œ cy cx œ cy ca"cy b œ c" # œc h œ † Šww # dy c$ y †dx ‰ b tan † c cince yw † ‹ œ Ê Ê œ y( b œ y y y y y dt 6 2 œ 1(x (7t)d œ x#y 4dx1xybcos xb b 2x sin% dx bdx a ac2 cosc$ xbdxcsin x)b b cosc# x en by yd c "Î# c 1) Ê a œsin x # c% 1 dy " x x 2c d 8 sin 2t c& d ( # "Î# dr ‰b 41. 2 a"Î# ‰(2 cos 2t)dy(2) x cosÈ% #b#tan a Èc ‰ œ $ dt (1 ˆ dy" x b c ˆ2 dy "Î# c& Ê tan y # b ) cos 2È a † œ dyb4(1#È cos 2x d œ x 2 dy Ê1‰s†) dx ˆs1x ‰ )#dyb50.65)œ d(1dy )Èsecc"ˆxxb) 2xfunctioncscdd)b )# Šx dycÈx‹sec‰ x2is b1Ê È(xy)Èxcos 2t)csc(csin c y† dt (2t) œ (1 b cos 2t) œˆ2x a and(csinˆxy ).4ˆ)#dy b bbcos secant‰w2xyacxbb†2xˆsin‰bx#2t) c#†yxc"Î# bccos1 ‰ c tan4(1#bc‰ cy # (xy) 2t) ) c c (xy) x cos b x b cos 2#È 2t) œ the minimum # in $ 2xyÊ Ê c dt œ c can have in c "  xÊ œ ˆ x csc# x‰c x œ ˆ# 28.smallestdx Ê 2(3xy dx 7)(3x) y bœ x y dec † Š3x Step3y‹ œ 61 valuex‰ the2:y œœ cot axy thedx œ y sin cˆ1 c 6 dy œ c6y(3xy b 7) dxx # c x œ xx dx x sin 3xy b 7) 4 b dx dx # dx b ) dx dx (cot csc b (2) "Î$ dy (2) of)(cos 2)and that # bcotb cot)dyww #Î$œ1sin )Êsec# csc1)))b 2# yc"Î$sec#)ˆc"Î# )Êdy„ 2cyc"Î$(xy) 1xc 2 "xccy"Î# Ê yw œ dy œ c x a) sin #) (csc w cot ) a œ 38. )3:)#Î$b csca )# 2 csc a1##b)2bx2xy b " ) cos (2 1x Ê#dy < y csc c$ "‰ Ê "Î$ 0. y y(3xy ) È c 4x œˆ 0 œ c ˆy‰ ; "1 ue b ybis 1 )) costep occursdyœxcb.6(cscb)œ3c‰("Î$‰cby32xcœ ‰dx)œcos‰a(cbdx ˆ11c<Èx‘ ˆ b ˆ‘ 3 x x œ ‰“ when3 ’œbc b cot ) # ˆ Ê 1 S (cscx Ê b))<x b#x2xy#7)(xy)‘ˆ)c3xy c <csc#$Î# b x ‘ Ê c$œ 3 œ sec‰ œ4 cœ c dx dy dx œ # y c # t c œ œ dy 7y 1 Chapter ccotcsc‰‰1 #...
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