MAT2500-01 13S Final Exam Print Name (Last, First) _________________________________|__
Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC). Use technology to check any integrals you set up.
1. Given the point 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, find the new coordinates, in each case stating the angles both in radians (exactly, using inverse trig functions) and in degrees (1 decimal place accuracy) and use proper identifying symbols for all coordinates: a) cylindrical coordinates. b) spherical coordinates. Support your work with two diagrams, one of the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= plane and one of the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= half plane, each including a reference triangle locating the point with respect to the axes with all three sides labeled by their lengths and both axes labeled by their coordinate labels and showing the relevant angles. Show clearly how you obtain values of your coordinates from these diagrams. Do the angles look right in these diagrams?
-%%PLOTG6+-%'CURVESG6%7dw7$$"1\kS++++I!#:$"1j^p********R!#:7$$"1D9hI`'G(H!#:$"1c%[2#z??S!#:7$$"1(*>l9[9\H!#:$"1&3Y@+Tw.%!#:7$$"2_eEz_YB#H!#;$"1KaZ$4zq0%!#:7$$"1mK_;7C&*G!#:$"1eb])Rmk2%!#:7$$"2$f2IJq8oG!#;$"1ba0i<e&4%!#:7$$"1b"=R@&*G%G!#:$"1CV*z<VJ6%!#:7$$"2bmfyZXm"G!#;$"2DytG1j68%!#;7$$"2&\52LyP*y#!#;$"1&R)fJIi\T!#:7$$"2YmKdBx?w#!#;$"1"*o1)oWy;%!#:7$$"2MuU"R5(Qt#!#;$"1B_R*\+k=%!#:7$$"1o<[6P#*3F!#:$"1,hB&Q'e-U!#:7$$"2Pk%=8Vs!o#!#;$"1s9&y%*H1A%!#:7$$"2N:'H1#)G_E!#;$"1<wp:sbQU!#:7$$"2%G,P,8xCE!#;$"1;mD'>_cD%!#:7$$"2;_d!Hyo*f#!#;$"2&\^%)G8-rU!#;7$$"1fZ'=5W(pD!#:$"1"*Q3[U5*G%!#:7$$"19&HUPzUa#!#:$"1$\.IkeUI%!#:7$$"2&*yv]YXX^#!#;$"1_(3Rb'p@V!#:7$$"2xaI#fh7)[#!#;$"1Vk!=rgpL%!#:7$$"0;'HMM.fC!#9$"1ve!y3ANN%!#:7$$"2P5AD!yAJC!#;$"13Nd]56pV!#:7$$"2kS<J@5@S#!#;$"02C4<(=&Q%!#97$$"2'4Ol>vFvB!#;$"2&p'Qa;z(*R%!#;7$$"2;t[u\NiM#!#;$"1'3)eFXL:W!#:7$$"1'z5$e6'fJ#!#:$"1w]8$>*GJW!#:7$$"2jPiI))=&*G#!#;$"1')=&e!)3]W%!#:7$$"1b?vU#p3E#!#:$"1"H*G>"\'fW!#:7$$"0'*oJ1t6B#!#9$"1buXl+euW!#:7$$"1eSg@d--A!#:$"16uROd**)[%!#:7$$"2efpi]NP<#!#;$"19F*Q#Hw-X!#:7$$"1%fmtDBA9#!#:$"1%=S$Q,%y^%!#:7$$"2j&oJh)=Q6#!#;$"1atr+'*>JX!#:7$$"2([9[s"*R$3#!#;$"1h/`OlEXX!#:7$$"2X(3\NNvb?!#;$"1*f;8#p$yb%!#:7$$"2%)G%H3GWD?!#;$"1,)pWD(QrX!#:7$$"2#QXf+7%o*>!#;$"1X"pB,`Re%!#:7$$"216z#p4'o'>!#;$"1J#HRb'*of%!#:7$$"2KDdrpou$>!#;$"1(oGYnh$4Y!#:7$$"18I/%48m!>!#:$"2:-pD85Ai%!#;7$$"2F"RK@\"o(=!#;$"1Wu2p%*QMY!#:7$$"2'))R'y`hi%=!#;$"1.x+BfkYY!#:7$$"22b7c5#)e"=!#;$"1ZMOb>geY!#:7$$"2-Q`lF)*yy"!#;$"1t%))G@8%pY!#:7$$"2Pq'yalub<!#;$"1>.u!Q(f"o%!#:7$$"2YTH")G>ps"!#;$"0*QT5vI#p%!#97$$"0U$px96'p"!#9$"1)e`7@JNq%!#:7$$"2j"G&)Qhbm;!#;$"1ef$RG%39Z!#:7$$"22-s%f=mL;!#;$"1)>)e1XeDZ!#:7$$"2;4r!oO60;!#;$"1Gt&HWd`t%!#:7$$"1Bx$>WSEd"!#:$"1A2`K3CYZ!#:7$$"2#ys19.)Ha"!#;$"17-S6f'fv%!#:7$$"2P$)4X(zY5:!#;$"1%*fk\8RmZ!#:7$$"1%3gYmeB["!#:$"1(yS493_x%!#:7$$"2.K61#GG]9!#;$"1#\Iq^Z]y%!#:7$$"2$>-z=rB>9!#;$"2vACmHZVz%!#;7$$"1DiHI@:)Q"!#:$"1*ytSxRM![!#:7$$"2rz:KdBrN"!#;$"1$pJ0P)H7[!#:7$$"14'oKfhsK"!#:$"1`L#f%*>1#[!#:7$$"2Q&HZ\E#\H"!#;$"1,H*yM2%H[!#:7$$"2B#fGJr/k7!#;$"1H7xu/eP[!#:7$$"2LQc*=k\J7!#;$"1#Qf`5pf%[!#:7$$"1[5lZ@)>?"!#:$"1L"yC(RP`[!#:7$$"2h:`#4;Jp6!#;$"0Z,ah[8'[!#97$$"2*=yg3$pz8"!#;$"1Y_tN2yo[!#:7$$"2vuY!Qil16!#;$"1mTCMM*f([!#:7$$"12?FK3!R2"!#:$"2w-#\$47L)[!#;7$$"12@)[1*oV5!#:$"1TIz">e)*)[!#:7$$"2XE)3Unq75!#;$"1pJ(yboj*[!#:7$$"1%))HSk9Xy*!#;$"1#QG*R(GL!\!#:7$$"0J#f)>[RZ*!#:$"1a")e-RU4\!#:7$$"1\JWGL%f:*!#;$"1%>?u*QX:\!#:7$$"1%>!\Pr9K))!#;$"0e&o()\P@\!#97$$"1Z^ddu<M&)!#;$"1uy(>\Hm#\!#:7$$"1)>Yxd2i@)!#;$"1%)ypn>.K\!#:7$$"0j%=%4?.!z!#:$"1'R0$Q/>P\!#:7$$"1*41%R11iv!#;$"1QE'[V%[U\!#:7$$"1zQt)HmKE(!#;$"2N\Bvnjp%\!#;7$$"1O4fD3>=p!#;$"1bwNXt!>&\!#:7$$"1cv]$o(\1m!#;$"1bOV6?;c\!#:7$$"1rLpuh$yH'!#;$"2XM5eoy,'\!#;7$$"1kO.&*Qllf!#;$"1km41MGk\!#:7$$"1#)[tK*e=j&!#;$"1eQd>4=o\!#:7$$"1WF1'\LzK&!#;$"1Y%GC3K:(\!#:7$$"0`p*)Gg\+&!#:$"2vvuxI()[(\!#;7$$"1c7"RQm&*o%!#;$"1mVF)Qfz(\!#:7$$"2(*odwpjuM%!#<$"1yd0,P1")\!#:7$$"1ksy"e$G^S!#;$"2&))RAu+c$)\!#;7$$"2OYWx%R$4r$!#<$"20,&p_*4i)\!#;7$$"2M&HJl$H3R$!#<$"1/I'f-*[))\!#:7$$"2O2.e$*yO2$!#<$"1(3l`bV0*\!#:7$$"0Q58)=:cF!#:$"1R\`ZyR#*\!#:7$$"2$[yU#ez@V#!#<$"1j:-**43%*\!#:7$$"28iQ!))Gm)3#!#<$"1Uh_#eNc*\!#:7$$"2WKp[]/Ox"!#<$"1[9"pL`o*\!#:7$$"22*4p-A`i9!#<$"1lz#=agy*\!#:7$$"28Pk/nQ*H6!#<$"2NQZb2B()*\!#;7$$"06)GuG>!)z!#;$"1relCJO**\!#:7$$"2cDlmX:2+&!#=$"1C`>A*\(**\!#:7$$"1[;hB#)3r9!#<$"2&\v%*e$y***\!#;7$$!2.7<)fQS#["!#=$"1t'RZ-y***\!#:7$$!1FmDu:xO\!#<$"1VT#pFc(**\!#:7$$!1hpayMTL#)!#<$"2X1lI1A$**\!#;7$$!2a==MQiw6"!#<$"1E`ru1v)*\!#:7$$!2XXZ/Q5'[9!#<$"1fAU(3,z*\!#:7$$!2%=*eS%zo"y"!#<$"171uzX#o*\!#:7$$!1z7a()Q58@!#;$"20jpjzKb*\!#;7$$!2A(H![9'G?C!#<$"1-oez(QT*\!#:7$$!16E^q*e#QF!#;$"1[*psI'\#*\!#:7$$!1^onn**)p1$!#;$"1$Qlxq%e!*\!#:7$$!1^-)QNMXR$!#;$"1MV>GQY))\!#:7$$!1_I:]7IJP!#;$"13H"H&z0')\!#:7$$!1n7R)H&yFS!#;$"10')4T0v$)\!#:7$$!2(Hi&[5&QhV!#<$"1&zF#**>%4)\!#:7$$!2'ea?_z:'p%!#<$"1O.KZs*y(\!#:7$$!1^p>_Hd=]!#;$"1WE8q,vu\!#:7$$!1Y3T2X<6`!#;$"2Dun3S6<(\!#;7$$!1cKMUf')ec!#;$"1K<WGS(y'\!#:7$$!1Qc/v,>`f!#;$"1#=ud-LW'\!#:7$$!1877KaH&H'!#;$"1b1[Q4@g\!#:7$$!1X@)\Vnyf'!#;$"1a!>](pFc\!#:7$$!1CDw#z`&Hp!#;$"1&R_JY[<&\!#:7$$!1oEUM"4^C(!#;$"13YbD*Hs%\!#:7$$!1KiD&*Q/uv!#;$"1()4$4%4IU\!#:7$$!1n,0FQ"e(y!#;$"1B;Lb>eP\!#:7$$!1')R\gO)4?)!#;$"19`ZR`GK\!#:7$$!0%)4Y`m$Q&)!#:$"1bl93pbE\!#:7$$!1u$QYCM<$))!#;$"2Xj*[(R#Q@\!#;7$$!1"=I7'pA["*!#;$"1AeQmvf:\!#:7$$!1oWX`pzu%*!#;$"1Y>+BvS4\!#:7$$!0_O&)*o(Qz*!#:$"1aPoC=9.\!#:7$$!1@P7+4A55!#:$"1i%o>/#)o*[!#:7$$!26.\z+4W/"!#;$"11K1sWq*)[!#:7$$!2/Y6h5&3v5!#;$"12tW1:0$)[!#:7$$!13v:(e"z26!#:$"2l0NihNd([!#;7$$!2%o2%\d&QP6!#;$"1XagLr"*o[!#:7$$!2K5%yo:pp6!#;$"1@V82sDh[!#:7$$!2Mt!*4#>/+7!#;$"1flmvS&Q&[!#:7$$!2=Azso;<B"!#;$"0Y#oBJ"f%[!#97$$!2=4(oyPji7!#;$"1&Rn&f&\z$[!#:7$$!2%)GR*Gf%\H"!#;$"1=O%e5,%H[!#:7$$!1;<m#o6gK"!#:$"1sqd4R'4#[!#:7$$!2o)zeZSsd8!#;$"1awR*)*G@"[!#:7$$!2N)*QYp:"*Q"!#;$"1WVn27;.[!#:7$$!2ch[h<4zT"!#;$"0o&>)>SZz%!#97$$!2OT$z<p%3X"!#;$"1W7a5l([y%!#:7$$!2A@1(\([-["!#;$"1'4'z1E'ex%!#:7$$!2vWe"Gb`6:!#;$"0%*\1"H0mZ!#97$$!2PS=S5?9a"!#;$"2:Pw#3=ZcZ!#;7$$!1c#Gg)=`u:!#:$"1$feZp8cu%!#:7$$!2Lm4)HD9.;!#;$"1ljpH^-OZ!#:7$$!2D%[Lm]aN;!#;$"1sH&40L\s%!#:7$$!19y#3m4]m"!#:$"11(e.sIYr%!#:7$$!2/,rq%\;(p"!#;$"2NN5G>^Jq%!#;7$$!1-6Dwf%[s"!#:$"164^N+2$p%!#:7$$!2*HE:a%)Hc<!#;$"1nu(RO!R"o%!#:7$$!2%G"3F#\g'y"!#;$"1ci;F#3*pY!#:7$$!2LT6ig;o"=!#;$"1(\jseP#eY!#:7$$!2WE(4Q8%o%=!#;$"1VH)y]:kk%!#:7$$!2x8VrF8c(=!#;$"1LBSCf([j%!#:7$$!1)4PZPNm!>!#:$"1uS&>%4?AY!#:7$$!2nR>**)>7O>!#;$"0x2#4v#*4Y!#97$$!1*[^a"*pq'>!#:$"1Y/6Zr!of%!#:7$$!2=)>96'3]*>!#;$"1&pp5)3v%e%!#:7$$!2CcC=5+e-#!#;$"1@r&=$*G7d%!#:7$$!1k?vuq?b?!#:$"1T5'fN$3eX!#:7$$!1R23&[dW3#!#:$"1fb3#H"yWX!#:7$$!1uF#*4x"\6#!#:$"1%fL@#ooIX!#:7$$!2N^WZT))G9#!#;$"2;/N3oCv^%!#;7$$!21o<UL\9<#!#;$"1:9bre'Q]%!#:7$$!0$H'="G)G?#!#9$"1xM,*>v&)[%!#:7$$!1c&\2U]7B#!#:$"1%z$e"\TXZ%!#:7$$!2'4jXT"p,E#!#;$"1h'QW(R+gW!#:7$$!2xAN.f"[*G#!#;$"1'[bU,G]W%!#:7$$!1"\$*>%zL;B!#:$"0d"=^A4JW!#97$$!2'4pB?D([M#!#;$".L8_egT%!#77$$!11J&oV$4tB!#:$"1b!)zqv&4S%!#:7$$!1A[")oL<.C!#:$"1L@xHYg%Q%!#:7$$!1yGdeSiHC!#:$"1=Fp"3.+P%!#:7$$!2acHHPK+Y#!#;$"1T!4%)pdHN%!#:7$$!1U!))z#4P([#!#:$"1HKj-RRPV!#:7$$!10V3$4CV^#!#:$"1Y")))\`#=K%!#:7$$!21")[$\')>VD!#;$"1\J[%G(*[I%!#:7$$!2&oP=\`2sD!#;$"1'QB&fmq(G%!#:7$$!0b@+&zC)f#!#9$"1ThrAu*=F%!#:7$$!22*=!HoNfi#!#;$"1z*fs"Q$\D%!#:7$$!2'=\QN%\Gl#!#;$"1.`Utf?QU!#:7$$!2EU@D$Q!>o#!#;$"1"obsa!))>U!#:7$$!2`j!fh=%pq#!#;$"1(o([%>jQ?%!#:7$$!2G\Mq'3eNF!#;$"1x\p@MG&=%!#:7$$!2PVwyx'QiF!#;$"1Lj[M&Rw;%!#:7$$!1:'zWi@))y#!#:$"1cK1ho**\T!#:7$$!2B">y*ok^"G!#;$"1,W:#Gs@8%!#:7$$!2`db6f:>%G!#;$"1aX%[4?Q6%!#:7$$!1QH!)f/9qG!#:$"2NRf*H!yT4%!#;7$$!2j?7Hj+f*G!#;$"1@q$*yz*f2%!#:7$$!2i92pH;7#H!#;$"1b^&)oH*y0%!#:7$$!1i,VIJ:[H!#:$"18(3V:l$QS!#:7$$!1N]#e@,\(H!#:$"1\+mD;q=S!#:7$$!1vsk,+++I!#:$"2Mak()*******R!#;-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#""#-%'CURVESG6%7dw7$$""!!""$""!!""7$$"2%)oPv]"Gx:!#=$"1^-05?/.@!#<7$$"1Ryc8dm\H!#<$"1_/4=w)G$R!#<7$$"21;KkGbI\%!#=$"1Z&4>QS2*f!#<7$$"29=OsWvm/'!#=$"1T#['HRBi!)!#<7$$"1lIhA:"Hf(!#<$"2_2:I?)Q75!#<7$$"16C['Hqk-*!#<$"2:KkGPHN?"!#<7$$"2&Hf=PP3^5!#<$"2Dd9H)\W,9!#<7$$"2:JiC>(f/7!#<$"2&[(\**eHhg"!#<7$$"2MqS"G$=wN"!#<$"1rU&3xd,"=!#;7$$"2=Pu[P>]^"!#<$"2)Ge;Le-??!#<7$$"2Gc7DIeOl"!#<$"1<MoOx([?#!#;7$$"2CY#\)*Gt4=!#<$"2)\**)z>xHT#!#<7$$"2Qze<N[k'>!#<$"29Ryc8J>i#!#<7$$"27C['HFZ<@!#<$"2:KkG(pHBG!#<7$$"1He;LthaA!#;$"2`5@UWch+$!#<7$$"28He;`&p<C!#<$"1b5@USfBK!#;7$$"2'>RycT%eb#!#<$"1E_/4Az2M!#;7$$"1W([(\Qa;F!#;$"1e;Lm%e?i$!#;7$$"1)oPvI!zeG!#;$"20D]+T?<"Q!#<7$$"2Y"He;s&[,$!#<$"1`06A'4)>S!#;7$$"1:Ig?)pM;$!#;$"0-/3wfz@%!#:7$$"2/17C[J&=L!#<$"2/3;Kk3ZU%!#<7$$"1C['H\E4Y$!#;$"1KkGd'oXh%!#;7$$"2'=Pu[(=Xh$!#<$"1"He;Le$>[!#;7$$"2Y!4=Oz0uP!#<$"117C[s2K]!#;7$$"2b>RyEPH"R!#<$"0E_/p\s@&!#:7$$"1pPv]2$H1%!#;$"1C]+,5C<a!#;7$$"2kQxap))y@%!#<$"1\)pRf^Qi&!#;7$$"2jKlI"[[pV!#<$"1oPv](zf#e!#;7$$"2Pze<&=;;X!#<$"1"Ryc8\:-'!#;7$$"2nQxap@!zY!#<$"1\)pRf&pQi!#;7$$"18Fa3&e`#[!#;$"1<OsW8"QV'!#;7$$"1'Gd9H/;)\!#;$"1"Qw_0R@k'!#;7$$"1OtY$>'=B^!#;$"1:JiC\"4$o!#;7$$"1E_/4E(zF&!#;$"1,.17oHPq!#;7$$"1#e;Lc9OU&!#;$"06AW3'[Js!#:7$$"1e<NqB&ed&!#;$"1xc8F)pWV(!#;7$$"1JjE`EpCd!#;$"1T%)oPN#Hj(!#;7$$"1"Rycj90)e!#;$"1@X!4='oSy!#;7$$"1:JiC(*eIg!#;$"1([(\*H'yS!)!#;7$$"1sW*)yJ1%='!#;$"1'Hf=d<aC)!#;7$$"1(QxazliL'!#;$"1\)pRRa$[%)!#;7$$"1C['H>ChZ'!#;$"1JkGdA$[j)!#;7$$"1)[(\*p<kj'!#;$"1;LmKpb[))!#;7$$"1lIhAhyzn!#;$"1`2:I[rR!*!#;7$$"13;KknkKp!#;$"1ya4>!HNC*!#;7$$"1v],.R&*yq!#;$"/,-/_gQ%*!#97$$"1Z%*)y<49C(!#;$"0$f=PA@b'*!#:7$$"1D_/4N3#Q(!#;$"/.17!yF%)*!#97$$"1He;L,vTv!#;$"206AWomb+"!#;7$$"1">Qw#*oso(!#;$"2)e<N!>p\-"!#;7$$"0*zf>OWYy!#:$"2`18E[#>Y5!#;7$$"1"['HfWy$)z!#;$"2U'Gd%f/X1"!#;7$$"116AW'*>S")!#;$"19Gc_*f`3"!#:7$$"1uZ&4**)G"H)!#;$"2(pRz)>0b5"!#;7$$"1mLnM'zAW)!#;$"2b6BYGPc7"!#;7$$"1w_06[r#f)!#;$"2NqS"3`pX6!#;7$$"1-05?fBP()!#;$"2OtY$*yk\;"!#;7$$"1e;LmqY$*))!#;$"1@U%)3cz&="!#:7$$"1AW)onmB/*!#;$"2jD^-*)[c?"!#;7$$"1Qw_0l2*>*!#;$"2<NqS`VlA"!#;7$$"1Hf=Pm$4M*!#;$"1d9H=#eaC"!#:7$$"1zf>R'=x\*!#;$"2/8E_[ijE"!#;7$$"1AW)oZ))yk*!#;$"2hD^-8&Q'G"!#;7$$"1C\)pz#p(z*!#;$"2)*)zfR!fjI"!#;7$$"1\(\**)R;a**!#;$"2KjE`'=AF8!#;7$$"1Fa3nz#)45!#:$"1OsW*GPkM"!#:7$$"1.17%Q(eC5!#:$"2R!3;7l6m8!#;7$$"2nNrU`$)3/"!#;$"14=O7Z%yQ"!#:7$$"2a3<MOQc0"!#;$"2sW*)y"y^29!#;7$$"2([(\*Rzsq5!#;$"2:LmKDPwU"!#;7$$"1:Ig]O2'3"!#:$"0-/3?)4[9!#97$$"1sV([Mz,5"!#:$"2"He;$z0pY"!#;7$$"2\&4>eb@:6!#;$"2(RzexS&p["!#;7$$"2>Pu[JP,8"!#;$"2"He;`(\o]"!#;7$$"129Gc*)4Y6!#:$"2Ea3<%>8G:!#;7$$"1MoO8W=g6!#:$"2'yd:^D"pa"!#;7$$"22<Mo5Ok<"!#;$"1%*)ydZ"eo:!#:7$$"24=Os+-6>"!#;$"1T#['4g8)e"!#:7$$"2tZ&4\Jh07!#;$"2'pRz)>%[2;!#;7$$"2&3<M)G<7A"!#;$"2Y%*)y<(*GG;!#;7$$"2(Qxa\X)oB"!#;$"1&)pR*Rz"\;!#:7$$"2e=PuVR6D"!#;$"2V"He;f=o;!#;7$$"2&ze<&\xiE"!#;$"2$Ryc$**p$)o"!#;7$$"*w]5G"!")$"*on!3<!")7$$"1BY#\8lqH"!#:$"2t\**)z,UH<!#;7$$"2Fa3<-A4J"!#;$"2MsW*Gg*yu"!#;7$$"2'[(\*fr$oK"!#;$"29LmK@;"p<!#;7$$"2X"HeE#)zT8!#;$"2Eb5@Ik!*y"!#;7$$"209Gcy9mN"!#;$"1a3<9(>)3=!#:7$$"2Ryc88V9P"!#;$"1X!4=%3fG=!#:7$$"2W)oP0rc'Q"!#;$"2E^-09c([=!#;7$$"2;OsWE)f-9!#;$"1#['H>58q=!#:7$$"2&)oPvE(H<9!#;$"27D]+pH(*)=!#;7$$"1D]+rq!=V"!#:$"2nOtY4w!4>!#;7$$"2Db5@"yJZ9!#;$"029G3d(H>!#97$$"2AW)o(y%zi9!#;$"1c7D]IR]>!#:7$$"2"4=O#H'ow9!#;$"17C[c]"*o>!#:7$$"2^.29yTJ\"!#;$"2MrU&3d&3*>!#;7$$"2*)yd:(4"p]"!#;$"2&=PuGY@4?!#;7$$"21:Ige:I_"!#;$"1,-/[uoI?!#:7$$"0,-/)eQQ:!#9$"2mMpQ<"=^?!#;7$$"2:JiCs4@b"!#;$"2([(\*H'z%p?!#;7$$"2[&4>=Oan:!#;$"2'Rzed"e+4#!#;7$$"2[**)z>)zIe"!#;$"1E`1$4t26#!#:7$$"2Qw_0=U&)f"!#;$"2<NqSd*QJ@!#;7$$"2sX"Hox(Gh"!#;$"1w_0"p.0:#!#:7$$"2hAX!R9sF;!#;$"29Ig?D&Hq@!#;7$$"1kGd%ysIk"!#:$"2'=Qw7Pw!>#!#;7$$"2MqS")*[Pe;!#;$"1rU&3`m6@#!#:7$$"2.29G+:Tn"!#;$"1Fa3PL:KA!#:7$$"2%*)yd&*)yzo"!#;$"1'=Pu_Q1D#!#:7$$"2%ze<bje.<!#;$"1Ryct%[9F#!#:7$$"2E^-0!zD><!#;$"1$oOt'QM#H#!#:7$$"2sX"HQ.OM<!#;$"1w_0^/[7B!#:7$$"1;Kk)zu![<!#:$"2X&4>)Rm2L#!#;7$$"2BY#\=EQk<!#;$"2(\**)z:5DN#!#;7$$"1D]+"[(>y<!#:$"2jOtY(*H4P#!#;7$$"2v],.XnUz"!#;$"0,-/gcBR#!#97$$"2=S!3'4#\3=!#;$"1pQx%zA8T#!#:7$$"2Y#\)py)4C=!#;$"2%**)zfrJ@V#!#;7$$"2X$pQZ+'*Q=!#;$"1Y#\)Hn%>X#!#:7$$"2"Ryc8iYa=!#;$"1_/4=;isC!#:7$$"2c6BYr0(o=!#;$"1([(\>wg"\#!#:7$$"105?S\1%)=!#:$"2LnMpe'37D!#;7$$"2OsW*e)=+!>!#;$"2Y'Hfy%eL`#!#;7$$"2Gb5@z1R">!#;$"2.29Gsv=b#!#;7$$"2)4?SSh!*G>!#;$"1Y$pQ&[(=d#!#:7$$"2:Pu[$>SW>!#;$"2&Ge;8f`#f#!#;7$$"1mJjY:cf>!#:$"28AW)G([Fh#!#;7$$"2D^-0DHU(>!#;$"2MoOtm0Bj#!#;7$$"2=Pu[B:0*>!#;$"1He;8.-aE!#:7$$"1/4=;*[^+#!#:$"2c?T#))=`tE!#;7$$"29OsW\t2-#!#;$"2;['HfYO%p#!#;7$$"2nOtYoJ\.#!#;$"2c:JiCUKr#!#;7$$"2d:JiK5/0#!#;$"1u[(\V!)Qt#!#:7$$"2:He;_u\1#!#;$"1b5@i$*H`F!#:7$$"14=O-$)>!3#!#:$"17C[OxftF!#:7$$"1mKlIB3&4#!#:$"1)oPv5VMz#!#:7$$"2DZ%*)GXm5@!#;$"2nHf=P>U"G!#;7$$"2Y%*)yP?nD@!#;$"2Ef=PQHU$G!#;7$$"03;KQ>59#!#9$"2Oxa4^#paG!#;7$$"1sV([kRi:#!#:$"1He;$>')\(G!#:7$$"2`6BY[D-<#!#;$"1([(\zRj$*G!#:7$$"2=Qw_$[D'=#!#;$"2b<NqW1]"H!#;7$$"2(Rzex;f+A!#;$"2&>RyOA7MH!#;7$$"1%ze<uxe@#!#:$"2:Rycl.X&H!#;7$$"1T"GcX30B#!#:$"2W&3<u7,uH!#;7$$"1yb6$)RvYA!#:$"1Pu[x>n&*H!#:7$$"2d:JiT@3E#!#;$"1u[(\bGW,$!#:7$$"1;Kky!)ywA!#:$"2Y&4>QurNI!#;7$$"1_/4e*R8H#!#:$"2Dg?T%*>^0$!#;7$$"1KkGFuD2B!#:$"14>QOKMwI!#:7$$"2;Gc7^"*4K#!#;$"2(3<M[`l%4$!#;7$$"2Mu[(HIjOB!#;$"2wlJjq5b6$!#;7$$"226AW'>u^B!#;$"2V"Gc_flNJ!#;7$$"0(RzG5%oO#!#9$"2'f>RQ!)ybJ!#;7$$"2.;Kka%)=Q#!#;$"2oa4>1Ye<$!#;7$$"2OoOtlOjR#!#;$"2yd:Ja:^>$!#;7$$"1*zf>xf>T#!#:$"2b18EOYf@$!#;7$$"1v],L(\oU#!#:$"/,-W'*zNK!#87$$"1(Rzer?DW#!#:$"1'>RyG%pcK!#:7$$"1E_/HnqcC!#:$"1,.1s*3cF$!#:7$$"1JiCH\QsC!#:$"2X(\**QK^'H$!#;7$$"2`2:I">S([#!#;$"2-5?S)e`;L!#;7$$"2d7D]M#Q-D!#;$"1MoO$z4lL$!#:7$$"2xg@VYH!=D!#;$"1xa4>EPdL!#:7$$"017C.TC`#!#9$"03;K/)ewL!#97$$"1OsW\/?ZD!#:$"1['HfEniR$!#:7$$"2(*)zf*f'\jD!#;$"2ElIhY&*zT$!#;7$$"2'=PuG9DyD!#;$"28He;dowV$!#;7$$"2<Qw_+TLf#!#;$"2a<Nq+)ydM!#;7$$"1['Hfr'o3E!#:$"1kGda*[#yM!#:7$$"105?5CzAE!#:$"2LnMpacq\$!#;7$$"1)e<NiGyj#!#:$"1%yc8$[5<N!#:7$$"105?!Q]Fl#!#:$"2LnMp]+q`$!#;7$$"0/3;-7(oE!#9$"2lQxap#GeN!#;7$$"1nMpyuz#o#!#:$"2BiC\Ijqd$!#;7$$"1/3;s"\!*p#!#:$"1QxaHAt)f$!#:7$$"19Gcs]r8F!#:$"2a3<Mw'G=O!#;7$$"216AW@E#GF!#;$"2Q"Gc_\jPO!#;7$$"2<MoONIQu#!#;$"1*yd:ZS%eO!#:7$$"1sV([h(\fF!#:$"1He;`,LzO!#:7$$"1>Qw-DvtF!#:$"2%e<NqmL)p$!#;7$$"2F^-0c!*))y#!#;$"2NoOtu?&=P!#;7$$"1LmKDQm.G!#:$"2Q%)oPV=#QP!#;7$$"1c7D+#y'>G!#:$"29MoO$4dfP!#;7$$"2a<Nq3NN$G!#;$"1nNr#yY!yP!#:7$$"2;Qw_A]%\G!#;$"2`<Nq'pE*z$!#;7$$"2xa4>H6W'G!#;$"1(Rze0:#>Q!#:7$$"1uZ&4&yAzG!#:$"2$)pRzYq*QQ!#;7$$"1<Mo'>cS*G!#:$"2%*)yd&fT(eQ!#;7$$"1<Nqq,=4H!#:$"2jNrU*o!*yQ!#;7$$"1&**)zH8@DH!#:$"1E`1t<G+R!#:7$$"2<KkGL5*RH!#;$"2`4>QW!))>R!#;7$$"2#e;LO,UaH!#;$"16AW[oARR!#:7$$"2e=Pu(3$*pH!#;$"2V"HeOy!*fR!#;7$$"1v],`yS&)H!#:$"2)*4?S!Qa!)R!#;7$$"#I!""$"#S!""-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#""#-%'CURVESG6%7dw7$$!#I!""$"#S!""7$$!1BY#\=FU)H!#:$"1(\**)z&p*yR!#:7$$!2<KkGM.0(H!#;$"2b4>Q7r1'R!#;7$$!1yc8Z%p]&H!#:$"1/4='f#4SR!#:7$$!1Qw_XK`RH!#:$"2w^.2mx$>R!#;7$$!2#pQx%)32CH!#;$"1#\)pz6w)*Q!#:7$$!1w^.(HN(4H!#:$"1oNriqkzQ!#:7$$!129GE;*[*G!#:$"2Fa3<]b)fQ!#;7$$!2(oPv!GS&zG!#;$"2Y-05/(QRQ!#;7$$!0$f=n"QU'G!#9$"1tX"HA%)*=Q!#:7$$!1jD^i!)\[G!#:$"1<Mo;u*zz$!#:7$$!1W([(pTjMG!#:$"2$e;LEA^zP!#;7$$!1a2:5n->G!#:$"105?!G-(eP!#:7$$!2/7C[;bL!G!#;$"20;Kk)o!yt$!#;7$$!1w^.FFD)y#!#:$"1oNr-.n<P!#:7$$!2tT$om#QXx#!#;$"2'*)ydbVQ*p$!#;7$$!22<MoWI#eF!#;$"1%*)ydfSwn$!#:7$$!13;K%e:Wu#!#:$"2uZ&4z2AfO!#;7$$!2b7D]hX$GF!#;$"1MoO`TzPO!#:7$$!1JiCp479F!#:$"2Y(\**ez#)=O!#;7$$!2'3<MyU^)p#!#;$"2Z%*)yP!>!)f$!#;7$$!2()pRz,`Oo#!#;$"2#)f>R-/#yN!#;7$$!1%ze<&o9oE!#:$"1#Ryc8Hvb$!#:7$$!2w^.2N2Rl#!#;$"2lNrU8V&QN!#;7$$!1Gc7D"[&QE!#:$"1rT$o;k!=N!#:7$$!2(4>Q1UfAE!#;$"2&ze<vAz'\$!#;7$$!213;KF1(3E!#;$"1uZ&4.v#yM!#:7$$!1BY#\#pq$f#!#:$"2w\**)**eFeM!#;7$$!2:E_/86#yD!#;$"1:IgS[hPM!#:7$$!2vY$p=:0jD!#;$"2LiC\--uT$!#;7$$!207C["QQ[D!#;$"2.;Kk3XyR$!#;7$$!29E_/$y4KD!#;$"2`,.1WIhP$!#;7$$!2'Gd9\TY<D!#;$"1Qw_l)=mN$!#:7$$!28Fa3dR=]#!#;$"2;OsW4'yNL!#;7$$!2lE`1Q"o([#!#;$"2&)oPv]3pJ$!#;7$$!2vZ&4RF?sC!#;$"2(pRz=.F'H$!#;7$$!2<MoOaQwX#!#;$"2')yd:R^oF$!#;7$$!1C['Hw9CW#!#:$"1KkG<IbcK!#:7$$!1nLnM2`FC!#:$"2d:Jik2nB$!#;7$$!22;Kk`[>T#!#;$"2ua4>QJf@$!#;7$$!2')oPv-TpR#!#;$"1^-0q8#f>$!#:7$$!2Eb5@o$f"Q#!#;$"029GCea<$!#97$$!28E_/UtjO#!#;$"2[,.1ck^:$!#;7$$!2v^.2e(Q_B!#;$"2nNrUx;l8$!#;7$$!29D]+BejL#!#;$"2'oOt1V9:J!#;7$$!2NpQxQ@?K#!#;$"2Z#\)p^Gg4$!#;7$$!1RycB`t1B!#:$"1_/4)4Zc2$!#:7$$!2F\)p4Y5#H#!#;$"0*zfz%Rh0$!#97$$!2a06A3feF#!#;$"129Gw(yW.$!#:7$$!2vZ&4\;zhA!#;$"0(Rz)>Ad,$!#97$$!1<Mo')\#eC#!#:$"1*)yd:LV%*H!#:7$$!22=Os5t7B#!#;$"22C['43.vH!#;7$$!1,-/QcN:A!#:$"2X$pQ<v!Q&H!#;7$$!2;NqSb@;?#!#;$"2a8FaS&\NH!#;7$$!2$*)ydN+)f=#!#;$"2c=Pu/SY"H!#;7$$!2D_/45r3<#!#;$"0.17![\%*G!#97$$!2MmKl.sd:#!#;$"2X)oP:FOuG!#;7$$!2DZ%*)=&G29#!#;$"2lHf=p/V&G!#;7$$!2(\**)zSwi7#!#;$"1mKl5_.NG!#:7$$!1MoO$H`16#!#:$"2'yd:"R/U"G!#;7$$!2wb6BLjd4#!#;$"2Ku[(46N%z#!#;7$$!1OsW\B4!3#!#:$"1['HfYcMx#!#:7$$!129GOj!f1#!#:$"1V&3<yTXv#!#:7$$!1-/3O"G-0#!#:$"2'pQx9vjLF!#;7$$!1e:J_6@N?!#:$"1W([(p[h8F!#:7$$!2v],.sI--#!#;$"2(4?Sg4k$p#!#;7$$!1D]+,Oe/?!#:$"1nLnM"yFn#!#:7$$!1tX"H.s,*>!#:$"2Pw_0riNl#!#;7$$!1(Rzeh7a(>!#:$"2d>Ry[$)Qj#!#;7$$!2LkGdY;"f>!#;$"1">QwGb@h#!#:7$$!2Y"HeO;OW>!#;$"1`06#=#[#f#!#:7$$!28D]+1s#H>!#;$"2$oOtYFOsD!#;7$$!1&)pR\j#R">!#:$"2'zf>*z,>b#!#;7$$!1Gc7b1#)**=!#:$"2/<Mo?%4LD!#;7$$!2^/4=W%y%)=!#;$"017C#f/8D!#97$$!2"Gc7&oi)p=!#;$"1rT$oC]J\#!#:7$$!1$f=P/,R&=!#:$"1d9He!o=Z#!#:7$$!1mJj'e:)R=!#:$"29AW)[u3`C!#;7$$!2$He;$*QcB=!#;$"2b5@U_=9V#!#;7$$!2">Qw#*z*)3=!#;$"2(e<N!*R'=T#!#;7$$!2F_/4&oQ%z"!#;$"0.17!e^#R#!#97$$!2:He;r#yy<!#;$"1b5@#G5<P#!#:7$$!28E_/X:Jw"!#;$"1:Ig+1#3N#!#:7$$!2U"Gci0')[<!#;$"2`3<M39=L#!#;7$$!207C[]APt"!#;$"22;Kk+I;J#!#;7$$!*C\*=<!")$"*KK>H#!")7$$!1x`2l[$Hq"!#:$"2F]+,#)z0F#!#;7$$!2tX"Hyz2*o"!#;$"1w_0rR5_A!#:7$$!29D]+%G;t;!#;$"2%oOt'y$)3B#!#;7$$!2b3<Mx,#e;!#;$"1Z%*)ypN4@#!#:7$$!2&f=P9_QV;!#;$"1Y"HeG!=">#!#:7$$!2h@V'oobG;!#;$"2Z&4>e"49<#!#;7$$!2c6BY*GV8;!#;$"2u[(\fQC^@!#;7$$!2%Qw_N<S(f"!#;$"2w^.2)*o)H@!#;7$$!2:JiCt-Fe"!#;$"2%[(\*4.F5@!#;7$$!1v\**GH>o:!#:$"2LjE`!R#44#!#;7$$!2vW*)y=#o_:!#;$"0$f=<HCq?!#97$$!2yb6B@0s`"!#;$"2Nu[(\pg\?!#;7$$!24>Qwq8L_"!#;$"2ve<N%\3J?!#;7$$!2\'Hf=#eo]"!#;$"2jGd9HW"4?!#;7$$!26@U%G!*3$\"!#;$"2:Gc7P&y!*>!#;7$$!2%\)pRT%)pZ"!#;$"2#*zf>b7$p>!#;7$$!0*zf>Thh9!#9$"2KlIh#)=)[>!#;7$$!2&)oPvF!*yW"!#;$"28D]+P?0$>!#;7$$!2_/4=QcCV"!#;$"2-17C%=%*4>!#;7$$!2_+,-=?pT"!#;$"2MnMp!pA*)=!#;7$$!2iBZ%>yX,9!#;$"2$['HfU5'o=!#;7$$!2Ga3<BArQ"!#;$"2OsW*3j\\=!#;7$$!2Rxa4cyAP"!#;$"2%)pRzu/(H=!#;7$$!1OrU:s#pN"!#:$"26=OsGO#4=!#;7$$!2mHf=5D;M"!#;$"2)Gd9pM$))y"!#;7$$!2(Hf=(*\)eK"!#;$"2Gd9HmYyw"!#;7$$!216AW5@?J"!#;$"2U"Gcs9O\<!#;7$$!217C[k8kH"!#;$"22;Kk_^&G<!#;7$$!2u[(\*4U2G"!#;$"2kJjE8cwq"!#;7$$!2Ga3<mRcE"!#;$"2PsW*[&>vo"!#;7$$!1%yc8?D>D"!#:$"2b/4=gL#p;!#;7$$!2x`2:Q<cB"!#;$"2.05?%)*[Z;!#;7$$!1v\**=D!=A"!#:$"2LjE`-q!H;!#;7$$!2D\)p\Dt07!#;$"0*zf*RVwg"!#97$$!2#)f>R!z]">"!#;$"248E_?x')e"!#;7$$!2a2:I@,f<"!#;$"215?SGoyc"!#;7$$!2b18E&*R5;"!#;$"1a2:qK0[:!#:7$$!24;KkyLb9"!#;$"2xa4>Qyt_"!#;7$$!2W)oP&G%HJ6!#;$"2B^-0Q#R3:!#;7$$!1&**)zf]$f6"!#:$"2nKlIT8z["!#;7$$!2kFb59")**4"!#;$"2_.29_TmY"!#;7$$!2sW*)y?$4'3"!#;$"2&Hf=xU7[9!#;7$$!2-*zffQ4r5!#;$"2MlIh9D"G9!#;7$$!2&Gc7l!)fb5!#;$"27<Mo3kuS"!#;7$$!1MoO`%Q//"!#:$"2(yd:r7D(Q"!#;7$$!2v[(\\2xD5!#;$"2mJjEL%pn8!#;7$$!2#Gc7lZ[45!#;$"1rT$oozfM"!#:7$$!1e4>Q3^[**!#;$"2Wze<6okK"!#;7$$!1'Qw_0lAz*!#;$"1=NqS`j08!#:7$$!1LjE`Jo]'*!#;$"2W%)oPvdnG"!#;7$$!1V%)oPn*e\*!#;$"2c7D]c>hE"!#;7$$!1&3<Mya-N*!#;$"2X%*)yP1qY7!#;7$$!14>Qwp,)>*!#;$"2xe<NE-kA"!#;7$$!1QtY$pw"\!*!#;$"2;JiC*ob17!#;7$$!1v_06ZN$*))!#;$"2LqS"G1y&="!#;7$$!1a06A'zKu)!#;$"129G;1xl6!#:7$$!1)>Ry;1)*e)!#;$"2kAX!*[2`9"!#;7$$!1"Gc7b.wV)!#;$"21<Mo!Q,D6!#;7$$!1Z)oP:XxH)!#;$"18D]?gO16!#:7$$!1#=Osk^u8)!#;$"2U#['Hb$*\3"!#;7$$!1.17CK3%*z!#;$"2.3;Kwxe1"!#;7$$!1i?T#eA7%y!#;$"13;KWj\X5!#:7$$!1"f=PW:\p(!#;$"2a9Hes))f-"!#;7$$!1AU%)o,YKv!#;$"2Gc7D-GV+"!#;7$$!1V%)oPey"R(!#;$"1c7D]Wrb)*!#;7$$!1Qyc8#>@B(!#;$"0X!4=c#Gk*!#:7$$!1za4>/g'3(!#;$"1sRze0!)[%*!#;7$$!1"oNrsDu#p!#;$"134=OwcO#*!#;7$$!1%=Pu)[3!z'!#;$"18He;lW`!*!#;7$$!1mD^-(pOj'!#;$"1@MoOH*[%))!#;7$$!1$*)ydN!e#['!#;$"1d=Pu/WV')!#;7$$!1-.17(*eJj!#;$"1,/3;'>@W)!#;7$$!1(Ryc`a6='!#;$"1HX!4QR:C)!#;7$$!1kJjEMjOg!#;$"1>U%)oX%)[!)!#;7$$!13?S!G-/)e!#;$"1X$pQPO0%y!#;7$$!1\#\)pE]Jd!#;$"1)**)zfN+Uw!#;7$$!1Hg?TGzub!#;$"1Q!3;7dIV(!#;7$$!0uZ&4F$HV&!#:$"1')pRz-"RC(!#;7$$!0pPvq]hF&!#:$"1`-05w'[.(!#;7$$!1Z#\)p3)f7&!#;$"1&**)zf6kMo!#;7$$!1V([(\l<w\!#;$"1d;Lm?!\j'!#;7$$!1BRyc`q>[!#;$"1J_/4QFEk!#;7$$!1*Rzen*evY!#;$"1)>Ryc>TB'!#;7$$!0kFb]&*z_%!#:$"0_.2MFt.'!#:7$$!1.,-/S.lV!#;$"0Z$pQ`/?e!#:7$$!19Gc7d[<U!#;$"1&3<MG9Li&!#;7$$!2L=Os%**emS!#<$"1W#['H*>@U&!#;7$$!2$>NqSG88R!#<$"1f8Fa/^<_!#;7$$!1[**)z*e2sP!#;$"1kKlIXVH]!#;7$$!2$>T#[w8<i$!#<$"1f@V'o^*G[!#;7$$!2%\**)z>'\sM!#<$"2cE`1$\**HY!#<7$$!/'>RyzGJ$!#9$"1LhAXI<<W!#;7$$!2/LlI@D?<$!#<$"2Mx`2&pOHU!#<7$$!28'>Ry#3&4I!#<$"1:E_/xn7S!#;7$$!1f=Pu#\G'G!#;$"2c9HeOKr"Q!#<7$$!2X*)yd&yt<F!#<$"1f=Pu/lBO!#;7$$!1$e;LY'phD!#;$"206AWG&f:M!#<7$$!20Gc7&Q-0C!#<$"12<Mo%)p1K!#;7$$!2)4=Os\ZiA!#<$"18C['HLm,$!#;7$$!2G([(\R%46@!#<$"2O;Lm_#z9G!#<7$$!2&pOtY<Oj>!#<$"1f:Jic"yh#!#;7$$!2&Qu[(*z@.=!#<$"2Xe;Lm!H/C!#<7$$!2dC['H"\Ym"!#<$"2vKkG<K&>A!#<7$$!1%=Osu(\0:!#;$"2`C['H.L2?!#<7$$!2J_/43()eN"!#<$"24.17W\y!=!#<7$$!2/E_/\@x?"!#<$"2Q,.1K&H5;!#<7$$!2$He;L!Q%f5!#<$"2d5@U/%e79!#<7$$!0G['HH)>3*!#;$"2uV'Gd5$4@"!#<7$$!1@05?q')yu!#<$"1htY$pA=(**!#<7$$!2:$yc8n'*3g!#=$"1T/4=c&>,)!#<7$$!1xT$oO')zb%!#<$"1-*yd::t2'!#<7$$!2VU"GcA"p+$!#=$"1m&3<M;#4S!#<7$$!2e]#\)p9#f9!#=$"2x+!*zf>c%>!#=7$$""!!""$!"!!""-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#""#-%%VIEWG6$;$!#N!""$"#N!"";$""!!""$"#b!""-&%&_AXISG6#"""6'-%+_GRIDLINESG6#%(DEFAULTG-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#"""-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6'-%+_GRIDLINESG6#%(DEFAULTG-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#"""-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6%Q!6"Q!6"-%%FONTG6%%(DEFAULTG%(DEFAULTG"#5-%(SCALINGG6#%,CONSTRAINEDG-%%ROOTG6'-%)BOUNDS_XG6#$"#]!""-%)BOUNDS_YG6#$"$g%!""-%-BOUNDS_WIDTHG6#$"%+R!""-%.BOUNDS_HEIGHTG6#$"%!3$!""-%)CHILDRENG6+-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"$D*!""$"$I'!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"$!y!""$"$5&!""7$$"$!H!""$"$S#!""%'CLOSEDG-%*PARAGRAPHG6#Qc\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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"%09!""$!%DX!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%g7!""$!%!p%!""7$$"$!H!""$"$I$!""%'CLOSEDG-%*PARAGRAPHG6#Qc^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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"%DI!""$"%gD!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%!)G!""$"%SC!""7$$"$!H!""$"$S#!""%'CLOSEDG-%*PARAGRAPHG6#Qc\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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"$v*!""$"%qD!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"$I)!""$"%]C!""7$$"$!H!""$"$S#!""%'CLOSEDG-%*PARAGRAPHG6#Qc\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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"%b<!""$"$v&!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%g;!""$"$g%!""7$$"$!>!""$"$I#!""%'CLOSEDG-%*PARAGRAPHG6#Q[_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"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"%lM!""$"%0M!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%qL!""$"%!H$!""7$$"$!>!""$"$I#!""%'CLOSEDG-%*PARAGRAPHG6#Qg]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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"%&z#!""$"%&3$!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%+F!""$"%qH!""7$$"$!>!""$"$I#!""%'CLOSEDG-%*PARAGRAPHG6#Q[_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"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"%]B!""$"%]9!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%g@!""$"%]8!""7$$"$!Q!""$"$+#!""%'CLOSEDG-%*PARAGRAPHG6#Q[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"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"%!4"!""$"%I9!""-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"$+*!""$"%I8!""7$$"$!Q!""$"$+#!""%'CLOSEDG-%*PARAGRAPHG6#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6"2.a) Describe the 3 curve segments comprising the counterclockwise directed curve LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, first in Cartesian coordinates as function graphs (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= as a function of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=), the middle segment being an arc of a circle centered at the origin. Then describe them in terms of conditions expressed in polar coordinates. [Remember, you can use inverse trig functions to express angles exactly.] In each case state the range of the independent variable along each curve segment using inequalities.
b) What is the exact opening angle \316\224\316\270 of this sector of the circle enclosed by the curve C and what is its approximate equivalent in degrees? Evaluate the area of the sector 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, where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the radius of the circle. Approximate this to 4 decimal places.
c) Let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW9HRiQ2LVEiK0YnL0Y2USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZRRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiNRIUYnRj4=be the right half of this region LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= enclosed by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Set up a Cartesian coordinate iteration of the integral 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 giving the area of the full region LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= as twice the area of its right half, and evaluate it exactly using technology, then approximately to 4 decimal places. Support your iteration with a diagram showing a typical bullet-endpoint line segment cross-section representing the inner integral with properly labeled endpoints and shading the region with equally spaced cross-sections.
d) Set up a polar coordinate iteration of the integral 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 over the full region and evaluate it exactly by hand, then approximately to 4 decimal places. Support your iteration with a similar appropriate diagram for these coordinates, as described above for the previous case.
e) Evaluate an iterated integral for 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 by hand using polar coordinates and evaluate exactly and numerically the ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbW92ZXJHRiQ2JS1GIzYoLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y0LyUrZm9yZWdyb3VuZEdRK1swLDE2MCw4MF1GJy8lLHBsYWNlaG9sZGVyR0Y2LyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0Y2RjctSSNtb0dGJDYuUSomT3ZlckJhcjtGJ0Y9L0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZYRlQtRkI2LVEiPUYnRkUvRkhRJmZhbHNlRicvRktGaW4vRk1GaW4vRk9GaW4vRlFGaW4vRlNGaW4vRlVGaW4vRldRLDAuMjc3Nzc3OGVtRicvRlpGYW8tSSVtc3ViR0YkNiUtRjE2JVEiQUYnRjRGNy1GIzYlRjBGNEY3LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkI2LVEiL0YnRkVGaG5Gam5GTEZcb0Zdb0Zeb0Zfby9GV1EsMC4xNjY2NjY3ZW1GJy9GWkZicEZmb0ZF giving the location of the centroid of the region on the vertical axis. Clearly mark it on the test sheet diagram.f) Evaluate the line integral of the vector field 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 around LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.
g) Green's theorem states that 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. Evaluate the right hand side for this vector field. Compare with previous results.
3. Consider the sphere 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 passing through the origin but not centered at the origin.
a) First express this condition in cylindrical coordinates. Make a labeled diagram of the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= half plane showing the circular cross-section of this sphere. Where is the center of the sphere in this diagram?
b) Express the equation for this sphere in spherical coordinates and indicate a typical labeled cross-section in the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= half plane showing the radial integration along LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy, and indicate the range of values of the polar angle LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy.
c) Set up the integral 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 in the usual spherical coordinates LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNigtSSNtaUdGJDYlUScmIzk2MTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUScmIzk2NjtGJ0Y0RjdGOi1GMTYlUScmIzk1MjtGJ0Y0RjdGN0Y3Rjc= over this sphere to evaluate its volume. Then repeat to find the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-coordinate of its obvious center 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 on the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-axis.4. 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a) Show that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNidRIkZGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHRjQvJSxtYXRodmFyaWFudEdRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYnLUkjbW9HRiQ2LlEtJlJpZ2h0QXJyb3c7RicvJSxwbGFjZWhvbGRlckdGNC9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRkcvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGRy8lKGxhcmdlb3BHRkcvJS5tb3ZhYmxlbGltaXRzR0ZHLyUnYWNjZW50R0ZHLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVi9GU0Y0LUYvNiNRIUYnRkM= satisfies the curlfree condition that it admit a potential function, i.e., is a conservative vector field.
b) Find a potential function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for it.
c) Use the potential to evaluate the line integral 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 over any curve from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUkjbW5HRiQ2JFEiMUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjJGJ0Y+RkAtRjs2JFEiM0YnRj5GPkY+Rj4= to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUkjbW5HRiQ2JFEiM0YnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjFGJ0Y+RkAtRjs2JFEiMkYnRj5GPkY+Rj4=. [If you want a check on this result, you can always do the line integral directly on a straight line segment.]solution (on-line)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC8lK2V4ZWN1dGFibGVHRj1GOQ==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The plots are not meant to be done with this sophistication by students who have only elementary Maple skills.1. cylindrical and spherical coordinatesa)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You have two choices for the angle, clockwise negative angle or counterclockwise positive angle: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reference angle down from the horizontal axis: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Above: a bit more than 45 degrees below the vertical axis.Below: exactly 45 degrees below the horizontal axis so 135 degrees down from the upward vertical axis direction: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b)\316\270 is the same of course.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. polar coordinate 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 is the plot: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The area of this sector in Cartesian and polar coordinates from the right half.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The area of the full region in polar coordinates.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Now the integral of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=: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and the ratio: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 this point with the sector:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJnBsb3RzRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQ=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3. spherical coord integralLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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4. conservative vector 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) Having a potential function means: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 necessary condition is 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.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY0LUkmbWZyYWNHRiQ2KC1JI21vR0YkNi1RKyZQYXJ0aWFsRDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRi1GIzYmLUYvNi1GMUYyL0Y2USZmYWxzZUYnL0Y5Rk4vRjtGTi9GPUZOL0Y/Rk4vRkFGTi9GQ0ZORkRGRy1GLzYtUSJ+RidGMkZNRk9GUEZRRlJGU0ZURkRGRy1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRidGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYG8vJSliZXZlbGxlZEdGTkZVLUklbXN1YkdGJDYlLUZZNiVRIkZGJ0ZmbkZpbi1GIzYlLUkjbW5HRiQ2JFEiMkYnRjJGZm5GaW4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYtUSI7RidGMkZNL0Y5RmhuRlBGUUZSRlNGVEZEL0ZIUSwwLjI3Nzc3NzhlbUYnRlUtRiw2KEYuLUYjNiZGS0ZVLUZZNiVRInlGJ0ZmbkZpbkYyRltvRl5vRmFvRmNvRlUtRmZvNiVGaG8tRiM2JS1GXnA2JEZdb0YyRmZuRmluRmFwRmRwLUZZNiVRIyUlRidGZm5GaW4tRi82LVEoJm1pbnVzO0YnRjJGTUZPRlBGUUZSRlNGVC9GRVEsMC4yMjIyMjIyZW1GJy9GSEZeci1GWTYlUSIlRidGZm5GaW5GZHBGVS1GWTYlUSlzaW1wbGlmeUYnRmZuRmluLUkobWZlbmNlZEdGJDYkLUYjNiVGYHIvJStleGVjdXRhYmxlR0ZORjJGMkZbc0Yyb) Partial integrating the first partial differential equation for the potential function leads 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Backsubstituting this into the second equation we get 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Partial integrating this leads to 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 backsubstituting leads 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We might as well set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, then we have the potential function: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Its difference in value between the final point and the initial point is the value of the line integral of the original vector field between those points on any curve between them.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If we parametrize the line segment from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNigtSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMEY3LUYxNiRRIjFGJ0Y0RjRGNC1JI21pR0YkNiNRIUYnRjQ= to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNigtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMkYnRjRGN0ZRRjRGNEY0: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with 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=pledgeWhen you have completed the exam, please read and sign the dr bob integrity pledge if it applies and hand in with your answer sheets as a cover page, with the Lastname, FirstName side face up: "During this examination, all work has been my own. I give my word that I have not resorted to any ethically questionable means of improving my grade or anyone else's on this examination and that I have not discussed this exam with anyone other than my instructor, nor will I until after the exam period is terminated for all participants."
Signature: Date: