ma1012_hw14_201012

Sec cy b3 tan1 2x b42yy dy 2yyd c2x dy yw c now to

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Unformatted text preview: $Î# œ (r ˆ 3x y c dr œ c 7) c 1 7x 16. g(x) œ 2 Ê (x) ) c † ( )] œ 35. bœ ) b cot ) Êb )Ê ( b 1)c% (1) b (xsin .(r c$ (4)(4x b $ dq œ ˆ ˆ # b ˆ 3 % b t sin t%) d 16(4x b 3)$ (x b 1) 3 t c sin t d) ) cos (r)) œ ), dy dˆc t ‰) 3) t #c3)(x sin ˆ5 sin ˆ t ‰‰ 231)csc "Î#ˆ# t ‰t‰È 3) (4) " c c3(4x‰dsin 5‰ (x dˆˆ1)‰d† b ˆˆ ‰ t cos # sin t dc # ‰ t 38. c # (4xsin ˆsin dy9c È œ ccsc )(cos t † dt Œ sin œ " ‰ # cos œ)cot3) ‰3t bb 7)Êœsin ˆ5 rb cos È 9 ) (sin 3 ‰t ) œ b)) 0 œ dt† wœ a2r c r bsin ) #3 a2r†d q r 2sinbŒ(21c‰2r)sin )dtcos(1 É1 b )3 tˆ t ) ccos ))(csin ‰)dt 3ccsc ˆ t ‰‰ ˆ dt 5cos É t ˆ œ Á 2y b f dr dx 2 b c () œ 3(4x )b ‹“ b116(x )b 1)dd) œ(rb 2x )b(4x 12 cos ) †2r c rb 1) c (x c 1) )) 2 1 ct dy 3) ˆ (xcos y) †(2x) 1 cos c1)œ dx œ c # "Î$ os ˆ 3 ‰‰ yÈ x(xb" †2 t2y dy " (x 2b (1 b cosœ w b ) " dy cos " 1) d 17.) (cos )25.29œœÉ1b 1ÈÊ)) œ dx)cbÉt b(xdrt )œ (sec )hb)1) œ))c(1dx œ y(x)bb tan † (csin 2))tan†)2 œ c 2 (sin ) (tan ) b sec )) 2))c#Î$ h( ) ) œ r$ . 1 b cos t(2Ètan ) œ cos È)1) Ê (x( tan Ê # b (sec 2))c#Î$ )) œ sec ) b sec ) 3 sec 2))(1 b cos (1 Ê x 24. c(sec ) b œ (sec ) b tan )) 3 sin (2 b 1) 2 sin ) dy )b œ dy sin ) d d) (sec ) b tan )) # d 2y œ 2x c)39.# (x c sinc(2x(x c Ê dy œ 2)sin (1t 2) d d ) 2x œ (1 b # 1 4 c Ê dt sin ( t 2) dr [ sin ( r c 2) † r b csc † dt dr dx 4b csin 5t) b cos(5t) 334œ y) cos))) t sin y) (# dx (1 † dt 36. œy1 rcossec c) œ r2)#Section 3.5drThe c # ) †œ rsin )1dand Parametric Equations c ) 153 (1tœ c rsincsc )) 3t c 1 ) 5t (c& r) d) c csc # dt Rule drcÊ œ) 2csin1tc )] œcos (1t # 2) Ê d) c 2) b r b Chain b ' ' dy cos. b cot " 5 c" 1 c œ dc) c tan ) $ % ab 2yd5xb tan% c x(x c y)1x1bb(cty)#2) ‰w‘ # (1t <1 2) tan b ‰‘ <4 tan$ 1)(2x d dtan# (2) (2x2 c in tancˆ$ cos 3 c b # c 5x 3 t# † dy x c< b Ê ˆ t œ # # sec< 5)y " (6) ax t c 5xb (2x5c"5) % ˆ atx" # # "Î% b (cˆ ) ‰w "c#5) 5 ˆ w t ‰‘ ## 3 y) œ 3 1 18. c1 )26. ‘yœ œ() sb 5))&Î%Ê # y xœ)3 ˆ1 b(sinÊc3x ‰b 2xy bˆ(1#b œ 1 c ycos œ ax#5)(sin ydw œ 5))"Î% c ˆ2xy " ‰# †ywdœ 1 c 3x c 2xy œ 2x k( dx#œ x œdtˆ1 b 1 xdÊ kwœ ) œ c y‰ (ˆ b 5))œ c cos x y 5) œÊ 1#ww () b b ‰ b () b 1 c"3x c 1 b Ê † y ˆ3‰ ) † x 1 b x ‰ 4 y Ê ˆc x 1† dx ˆ1 b x ‰ ) 49.‰ (sin x b(xx Ê 1 b ( œ x 4 ) 1#x dt 1 39. dt y‰ x x dx x x b 1 c# c$ w1x ‰ ac c5x t c1 t x(x # 1 (x ˆ y) d ‰ œ c # b xyt c2 c‰ b ‰ x b&gc t(xœ y) d # b1 bxcosc‰ c†y)d xˆ 1c 1cos t% 1xt a1 c# 1sin $c x t† (sin t)(# sint t) c (" b cos t)(cos t) y) (t) x c ˆ dy b 2xy c c b xx y # ‰‘ (1 tan # sec " " anc y) 1#2yÊ 5)dx 1# ‰tˆ†2y"# ‘x#œdt<1## sin‰t %œ ˆ#1#sec "<bˆcos wt)"1b‰ b ˆ 6ˆ‰## (sin t) " ‰% œ 6 ˆ1%b " ‰d b 6 x 1 b d ‰# œ c...
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This note was uploaded on 12/26/2010 for the course MA 1012 taught by Professor Franciscoperez during the Fall '10 term at ITESM.

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