ma1012_hw14_201012

Y dx 4 1 c sin 3 t cos 2 acos a bb 2 c2 sin a

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: tc 3 22.x dx xy "Î#t œ 1 Ê 3x c y c x dx c 3y " † d c 0 c " dy t)c c œ# c dy x c' & 19. ˆx cÈcb y œ (3wc t)"Î#ˆ Ê ‰dp c " b$Î# ˆc"Î#œ dt #Ê a3y"Î# xb dx œ y "Î# 3x 2 Ê" dx œ " dt # œ ax x cos xb b asincœxb ap #œ" ‰ bcc a aÊcos# xb (†csin" x)b #œ a#1(3$cbt)#3dx b ax(3b 1t)cœ c " (3 c # b 1bc$Î# È3 c#t b x#3y c x œ c b 1 3 3 3 y œ x c ax b cos x a x‰ 10. y x x x b b b † acx b "b # dy 2 È È 3dr y œ $ 2x œ (2x)"Î$ Ê dy œ " (2x)c#Î$ † 2 œ 3x b . 4. y )œ %) b5x œ (5x)"Î% Ê dx œ (cot csc )) dx 3 ) cotdr )c" Ê È œ c(csc ) ‰ ˆcot")‰c# dd) (cscathematics csc ) cotb cotcsc ) œ csc4. ) berivatives Part II ) ) " ‰ ) b cot )) œ È ) " )) # "b d) )‹ ˆ sec (csc‹ Š c ) b tan ˆM Šsec È) tan I: Homework 1(csc D cot )) ) È‹ d) œ Šsec ) ) œ sin a) b (csin 2x ) d) Ê)) bœ (2)) acos a) bb † d) a) b (2 cos x 1. y œ ) dx 4 1 c sin 3) t ‰ (cos 2)# acos a)# bb (2)) œ c2 sin a)# b sin (#)) b 2) cos (2)) cos a)# b # 2. y œ x Ê dx œc5x " 4 (5x)c$Î% † 5 œ 5 4x ) 161 149 ax b 1 b d d # # # # " " 35. cos# x sin Ê dr x cos d x sinc& œ (2r #œ sin a)# bxcos (2))t)$ d (1 œ sin a) b (csin 2)) (2)) b cos (2)) acos a) bb † d) a) b sec 1t)x† c (sec 1t) x b xsec 1t)(secœ ctancos: †xdt d) t) œ 21 sec# 1t tan 1td) 1t # 3c 1 # dt 23. x (x in y)# b cx 2) c y # "Î# c"Î# sin a)# b sin a# ) # c"Î# cos 20. qœ sÈa) c(r# sin a2r)(2) # b (cos 2)) acos " ) 2rbc r#)bœ c2 dr % 2r c r# b (#)" a2r c cos (2))(2 c a) bœ " c r œ 2r œ c rb Ê dq œ # a b (2) †da œ # b 2) rdrb 2r) 11. c" ( S#tep 1: Ê ’ds œ 7 y) Š1 c dy ‹“ dr (x c y)# (2x)c# 2x c 2y dyc$ œ )c$Î% Ê d) œ c 3 )c(Î% È2r c r s œ Èt œ t#Î( x# dt c2 tc&Î( 12. r œ È) 2(x d b œd8 4 dy " 7 y2)( b ˆ4 c " ‰ d Ê dx œ 21 (3x c 2)' † dx b c dx c& (csin 2t) "d (2t) dx ˆ4 c dx cos c& † dt (1 b cos 2t) œ c4(1(3xcos2) b3.61) ˆ4 c †#x ‰ †œ (1 bsin 2t x ‰ 2t) # Sectiondy(c Implicit Differentiation # " 161 È t œ c4(1 b #x 2t) dt # " cos 2t) dr ‰ 36. c#œ Šsec È)‹# (x c"y) Ê b 2y œ sec2x c 2x#d c) y)ˆc 2x(x c y) ˆ d Šsec 4) tan È)‹4Š " ‹ rˆ œ Step"2: c2x tan ˆ dy dy d ds Š œ È)‹ ˆ sec ‰ c " ‰ b tan ‰ (x #Î$ c 2)' c dx " )' † 3 b (c1) ˆ4 y œ "sinsˆœ x4 ‰ sinc3t b 54 cos 5t cos)ˆdt dxb345)cos 3t †† ˆdt (3t) (2t 54 )(csin 5t) †œ c 4 (2t b cos &Î$c 1 ˆ#È) b 5)c#Î$ ‰ 1œ 1 1 13. c 21. ‰ (2t3b 5) (3x‰ Ê# )dt œŠÊ (2t 1 c#Î$ ‰ c 2 ‰ b b 5)c&Î$ † 2 )dt (5t) œ 1 5)c3t cos sin 5t (2t #x 3 3 Rule and Parametric Equations dy x 4c ‹ 151 y dy cc (x c y) ˆ x œ c c ˆ Section 3.5 #The Chain c‰ y) c$ 4 3: dy c œ c21 1 b cot ˆ t ‰‰Step d cosbdxÈsin‰‰#œ"c2 b 2ydcot ˆ t"‰1c$ †È c y) È (x c d ˆ td‰...
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