722G^=,dd +(I)   1Courier New1Symbol New1Courier New1Courier NewTimes New RomanTimes New Roman1Courier New1Courier New1Courier New1Courier NewXDu6V8XDu6V8XDu6V8XDu6V8?/ <```@@@?~~~~~ԱޱޱԱ޿޿ph (((Pdd{ d<  p {2 h!4?ؑ?õp@Disn&X3@ǭEYO1 S,!@l7???8{t@pK @z@/kٮm!Ńғ@_xl@mmiUK[@033333??@^ߛOw?HzG???tXIc@`\V8@@?@ @@@O?wC~UwC~?@?@?@\ -P "2@[Y5@ڷ>u@@dddddddddddddddddddddddddddddddddddddddd 02??@$$$??\ -eÙ_@P "2@[Y5@t;@???``YW9$ƴT]E2e^t2te^tt^2-t+3-2.00000;1.00000Z' '2e^p,2pe^p,p^52??@$$$6,}iH??;P(.@r,`硡?e} @;P(.@r,`?e} @???;P(.@r,`?e} @ؖ0pDx%882e^a2ae^aa^2-a+3(x,y,z) = (2e^a,2ae^a,a^2-a+3)-p+3) to (2e^p+(-e^(42???$$$??NWp2`&?ڷ>u@???})\?,P40-ľ$pX߹@66ka2e^a2ae^aa^2-a+3 2e^a+TX(a)Cseg (2e^a,2ae^a,a^2-a+3) to (2e^a+TX(a),2ae^a+TY(a),a^2-a+3+TZ(a)) 2ae^a+TY(a)a^2-a+3+TZ(a)p)*(p+1)+2p^2-2p+.7542???$$$??NWp2`&?ڷ>u@???})\? $ XHjccܳc2e^a2ae^aa^2-a+3 2e^a+NX(a)Cseg (2e^a,2ae^a,a^2-a+3) to (2e^a+NX(a),2ae^a+NY(a),a^2-a+3+NZ(a)) 2ae^a+NY(a)a^2-a+3+NZ(a)`9`! B42???$$$??NWp2`&?ڷ>u@???})\?HȖXD@BsdHd{d2e^a2ae^aa^2-a+3 2e^a+BX(a)Cseg (2e^a,2ae^a,a^2-a+3) to (2e^a+BX(a),2ae^a+BY(a),a^2-a+3+BZ(a)) 2ae^a+BY(a)a^2-a+3+BZ(a)?0!j42???$$$??.[Tȯا? û?@@SS@???})\?kTh*e@ef2e^a2ae^aa^2-a+32e^a+RHO(a)*NX(a)Xseg (2e^a,2ae^a,a^2-a+3) to (2e^a+RHO(a)*NX(a),2ae^a+RHO(a)*NY(a),a^2-a+3+RHO(a)*NZ(a))2ae^a+RHO(a)*NY(a)a^2-a+3+RHO(a)*NZ(a) @OOxx52???$$$ rX@i[-@??Eubҵ@:bef@Eub@:bef@???Eubҽ@:bef@\a|\Heff2exp(a) + RHO(a)*Nx(a)2*a*exp(a)+RHO(a)*Ny(a)a^2-a+3 +RHO(a)*Nz(a)Q(x,y,z) = (2exp(a) + RHO(a)*Nx(a),2*a*exp(a)+RHO(a)*Ny(a),a^2-a+3 +RHO(a)*Nz(a))5O02??h!@$$$Uy@?׾T8llhQ`T?b}1TX#62EXP(X)(X+1)/NORMZERO(X)55uHh{1x $5X5\z50@42-55i5`TY$6(2X-1)/NORMZERO(X)5(55?42\5$555e05X?TZ2T%6(4X^2-8X+3-4EXP(2X)*(X+1))/NORMTHRE(X)*,5`59f5@42*55\z50?42-NX&6 (4X^3-9X+4+4EXP(2X))/NORMTHRE(X)42*d555?425$5NY5(6 -2EXP(X)(2X^3+3X^2-X-7)/NORMTHRE(X)42T2*5<5 1@55i5`@NZ42)6 -(2X^2+X-4)/NORMONE(X)5l55?42?5$555e05X?42TBX,*6(2X-3)/NORMONE(X)2*Qp559f5@42-5 5\z5042*?BY@+62EXP(X)/NORMONE(X)?UXU4842*?555?42?5$5D5xBZT,6(2X-3)/NORMTWO(X)42T25e#@p55@51#@p5H55 XPXxh-6 (2X^2+X-4)/NORMTWO(X)f5 555H 55f50@5L5ip@`@42*?XPY|.6 -2EXP(X)*(2X^2+X-4)/(NORMONE(X)*NORMTWO(X))42?5v55P5ef5X?42TYPX/62EXP(X)*(2X-3)/(NORMONE(X)*NORMTWO(X))2*5 55?42*T559@@4YPY*06-( (2X^2+X-4)^2 + (2X-3)^2 )/(NORMONE(X)*NORMTWO(X))42-$5X5ip@`42*55L5?YPZProject 2: Problem 4 Space Curvep/sqrt(4e^2p+4(p+1)^2e^2p+(pi̍9s@UAb(E@G1@@Times New Roman EUnit Binormal Vector is BluerveRdNOQRԅ? L5@ E@@Rɑ@Times New RomanؚEUnit Tangent Vector is Red(&Z d\hiDH+Ko?QDeZ@n}\@oQ@Times New RomanEUnit Normal Vector is Purple&&e`N?z.=ƌDH+Ko? O@u@,*Ւ@Times New RomanHECenter of Curvature is BlacklOlH $x 5T+?`I@j=@=“@Times New RomanEAnimate on A to Move on the TrajectoryXP(2((A)))))8(((A)))+,W[hMJ̓@ry Times New RomanEOsculating Circle is Fuchsiarajectory(A)))+1))^2)+2)+(2((DH+Ko?f#N@@sc@,A@Times New Romanx = 2e^t; y = 2te^t; z = t^2-t+30OP  @sؗܳ@1Courier New (E(x,y,z) = (2e^a,2ae^a,a^2-a+3) @d@@}審Rʽu@1Courier New Eseg (2e^a,2ae^a,a^2-a+3) to (2e^a+TX(a),2ae^a+TY(a),a^2-a+3+ @sj34\@1Courier New _aseg (2e^a,2ae^a,a^2-a+3) to (2e^a+NX(a),2ae^a+NY(a),a^2-a+3+ ;h)@Ts qz@1Courier New `aseg (2e^a,2ae^a,a^2-a+3) to (2e^a+BX(a),2ae^a+BY(a),a^2-a+3+ R⠷@HW[2Z@@1Courier New Taaseg (2e^a,2ae^a,a^2-a+3) to (2e^a+RHO(a)*NX(a),2ae^a+RHO(a)* g@P.q.(:mt@1Courier New ba(x,y,z) = (2exp(a) + RHO(a)*Nx(a),2*a*exp(a)+RHO(a)*Ny(a),a^ o_@gNv,H@1Courier New bax = 2exp(a) + RHO(a)*( Nx(a) + xpx(a)*cos(t) + ypx(a)*sin(t) дk@'r{i @1Courier New @@@h!@