ma1012_hw14_201012

R 3xy bx 3y 6y bb 3 23xytc3x 3xxdx tb 3y xc2t b6 c t x

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: œ ˆc 2y œ †1 ( ˆ1seccot)2x 5t) ˆ ‰ b 1 " tan 2x ‰‰secx(x)csc# ˆ t ) ‰ † Šsec )‹ tan È) tan ˆ ‰ c sec ˆ ‰ " 3t c ˆ t x dx b œc) sec c x(x c y) c È c y) d ˆ# x c1 c x(xcy) c (x c#y) œ dt x a# c x b xy c x b 2xy c y b tan ” • dt # dt # ) ) ) c d 2x c1 1 dy # (x ) #È ) Step 4: œ 1) œ " c 2y % z œ cos ˆ(" c 6t)#Î$ ‰œ# "Î# 2x (xcdy bˆ(" c$6t)#Î$ ‰ †y 2 (1(xc y) d c"Î$ œ ') œ 4(1 c " 6t)y "Î$ sin ˆ(1c"Î# #Î$ ‰ # d # c c c"Î# 6t) b dx Ê dz Ê 4 y) 2 (c t# b x y cx a1 c c 6t) sin at b † at b‰ dyy œ a1 b cos at c%b dt œ csin 2y" a‰ b cos at# bbx c † ˆc1 " ˆ 2 14. 2‰ 3 2 c$ c% cos"a‰ ˆb œ ‰$ b cos at# bb 47. a ˆb ˆ b 8 x b 1‰ Ê dxsœ c3(5 3ct ‰ b c 2xc2) tb cÊ x ds #œ1cos ˆ 31t ‰œ d ˆ 3c‰dtc 1 bˆ 3ˆ x‰ † dx ˆ 311‰ œ 31 cos ˆ 31t ‰ c 3 sin ˆ 31t ‰ 6(5 1t 2x) sinc 1t b #t 1 2x) b ( b 1 y xy œ dt 22. œ sin ˆ # œ x cos ˆ 33x ‰ 8dt dt 1 c x # # dt È # 2dÈ# 2 # 162 œ ChaptertcosDifferentiationb †t 2t œ #c † tdt t at #b 3 ax#y ccdqb yasin at# b 12 sin x"Î# " ˆ t b 1‰ t b 1 (1)ct † dt ferentiation Chain Rule1sinaŠ b 1t ‹ tÊb31t ‰Equations ‹ †149 d t cˆ1 b Š x b 1‹ ion 3.5 The 37. q œ andÈ3 b 1c sin dt "Î# cos Š Èt b 1 " dt È1 bb 1 ‹c"Î# Š"Ètc"Î# † Š Èt cos at bœ cos ‹ œ 3 # cosParametric œ c" c" t# # ˆÈ t b 1 ‰ 15. f(x) œ É1 2 Èx œ ˆ1 c x"Î# ‰ Ê f w (x) œ # ˆ1 c x"Î# ‰ d ˆc # x b 1 ‰ œ œ dyx dc ȉ Chapter # .5 3 4É ˆ 4 É c È x‹ È c 5)) † (dy œ (2t c c 4b $Î% t c c dt d (2t c ‰ c dt cos (2t ) 5) œ cos # "‰ # w œ cos (cos ˆ 34."5)) † 2Ȉ "œ 3 c#Î$#b tdy 1 c Ê "dr# c )c"Î# sinyˆ "3x b )dy"Î%(2t c 5) œ )c"Î#Šb1)c"Î$ b x c"Î% x 1 c x dtc y œ x# dy bsec# dy b sec Ê ‰a† d# ax xÈœ)x(cos (2t ‰ tan ˆ "dy †œd )c "Î$ 5)) † sec ˆÊ dr dy dy) ) ‰ x k (x) c "dx 3y24.r (3xy b"x 3y 6y bb 3 2(3xytcˆ3x † Š3xxdx tb 3y xc2(t b6 c t Ê x 2(3xy b 7)(3x) c 6 œ c6y(3xy b 7) y b 7) Ê ‰ 2 œc ‹ œ 1) dx "Î# œ c c 7) t dx c t)cxdx œ 0 os Š #dx ‹ † Êdx œ sec 1 xd) cos Š dx dx3yŠ xb 2x ‹ œ Š d)t b 2 ‹ cos Š t ‹ dx) b csc dx c t) cc csc c" t b sin (2tœ c5)) (3 dy 23. rœ 2(csc ) "t É ))È% Ê1 dr "œ œ (csc )ÈtÉc‹))c# bd1)(csc$ )É cotb 1) œ csc ) cot Èt bÉ) œ È ) (cot ) b csc )) d ˆ È È 2(t " db) %† ˆc " ‰ b#2x sec ˆ " ‰ œœ 4 % cˆŒ‰ cotb ˆ "9 tandˆ dy œ 4 cos Œ b 11$b Ètd) † d Œ b1 2(t Èt9 œ 4 ) b cot )) 1 b (csc )†b cot )) ‰ 48.19.œ dy3 (c x b cb 1) t † dÊ ) dt c y 2x sec t b 1 sec 9 [6x(3xy b 7) c 6] œ c6y(3xy bb cot dycœ c dt † dx 7) )œ (csc 7y 1 (x b x $ Ê dx œ (4x b 3) sin 3)(x1c"Î$cx ‰ dx (x xb 1) b (x b 1) (4)(4x b 3) y(3xy b(4x b 3) 3xy bcos Œ c%Î$ t9 É È † dt 1 b Èt‰ 1) x %Î$ # Ê2xc"Î#" b 1‰ 21 (r) ˆ )) csc ) Ê [cos (r))]gwr b œ dr ‰2œ2xc"Î#Ê 1) cos (r)c1)xcr cos c$)c2xc"Î# b 1‰ r cos xc)$Î# c r 1b t ˆ 0 7) cdr [dx ‰ dxœ x(3xy b c...
View Full Document

This note was uploaded on 12/26/2010 for the course MA 1012 taught by Professor Franciscoperez during the Fall '10 term at ITESM.

Ask a homework question - tutors are online