J.)=,dd +(I)  1Courier New1Symbol New1Courier New1Courier NewTimes New RomanTimes New Roman1Courier New1Courier New1Courier New1Courier NewP`NSP`NSP`NSP`NS?/ <```@@@?~~~~~ԱޱޱԱ޿޿ph (((Pdd{ d< p {2 ~- E?g@(ӇdƋ0;@`:nH@l7???8{t@pK@z@lۣte @v5@p*5@033333??@^ߛOw?HzG???nwH@@@?@ @@@?@@?@?@?@F2`@xGFڻ@ k@@02??@$$$??xpD?pX^%쟧@@t@@???ěȜ̝Оԟؠܡt 콰L#2e^t2te^tt^2-t+3!x = 2e^t; y = 2te^t; z = t^2-t+3Z' '2e^p,2pe^p,p^52??@$$$;͒p >??(59Ń?=M`(\@@@Od?`(\@???(59Ń?`7`(\@TӰ,B2e^a2ae^aa^2-a+3(x,y,z) = (2e^a,2ae^a,a^2-a+3)-p+3) to (2e^p+(-e^(42???$$$??NWp2`&?ڷ>u@???`#?ࢰ䣰褰쥰|02e^a2ae^aa^2-a+3 2e^a+TX(a)Cseg (2e^a,2ae^a,a^2-a+3) to (2e^a+TX(a),2ae^a+TY(a),a^2-a+3+TZ(a)) 2ae^a+TY(a)a^2-a+3+TZ(a)p)*(p+1)+2p^2-2p+.7542???$$$??NWp2`&?ڷ>u@???`#?  2e^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???$$$??NWp2`&?ڷ>u@???`#? ,Ʊ(Xl2e^a2ae^aa^2-a+3 2e^a+BX(a)Cseg (2e^a,2ae^a,a^2-a+3) to (2e^a+BX(a),2ae^a+BY(a),a^2-a+3+BZ(a)) 2ae^a+BY(a)a^2-a+3+BZ(a)?0!j42???$$$??_?ح)nip$@?Չ? @??? $(,8`aͲ2e^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???$$$&XZ???'?Pج/?8,rVv@`w@(dl֗Y?8,rVv@???'?(dl֗Y?8,rVv@ $(,0ȁ2exp(a) + RHO(a)*Nx(a)2*a*exp(a)+RHO(a)*Ny(a)a^2-a+3 +RHO(a)*Nz(a)Q(x,y,z) = (2exp(a) + RHO(a)*Nx(a),2*a*exp(a)+RHO(a)*Ny(a),a^2-a+3 +RHO(a)*Nz(a))5O02??h!@$$$Xy@? R?ȥDEN_=̴@ :¬@p0{i@q4@???048<@ D H ?<ԴԴ@մ;2exp(a) + RHO(a)*( Nx(a) + xpx(a)*cos(t) + ypx(a)*sin(t) );2*a*exp(a) +RHO(a)*( Ny(a)+xpy(a)*cos(t) + ypy(a)*sin(t) ))a^2-a+3 +RHO(a)*( Nz(a) +ypz(a)*sin(t) )x = 2exp(a) + RHO(a)*( Nx(a) + xpx(a)*cos(t) + ypx(a)*sin(t) ); y = 2*a*exp(a) +RHO(a)*( Ny(a)+xpy(a)*cos(t) + ypy(a)*sin(t) ); z = a^2-a+3 +RHO(a)*( Nz(a) +ypz(a)*sin(t) )_ xyzHXT@ QPy@?@?@@@@@@@@@@@@@@?@@@@@@@@@@ @ @ @SQRT( 4EXP(2X)(X^2+2X+2) + (2X-1)^2 )ۺeLXNORMZERO SQRT( (2X^2+X-4)^2 + (2X-3)^2 +4EXP(2X) )NORMONE SQRT( (2X-3)^2 +(2X^2+X-4)^2 )NORMTWOH (4X^2-8X+3-4EXP(2X)*(X+1))^2 reenMA (4X^3-9X+4+4EXP(2X))^2 +8)^2+(4P-6)^2+16E^(2P))))MB 4EXP(2X)*(2X^3+3X^2-X-7)^2 42*MCDSQRT(MA(X) + MB(X) +MC(X) )NORMTHRE 0.5EXP(-X)*NORMZERO(X)^3/NORMONE(X)1#&P&RHO2EXP(X)/NORMZERO(X)TX@2EXP(X)(X+1)/NORMZERO(X)TY(2X-1)/NORMZERO(X)TZ(4X^2-8X+3-4EXP(2X)*(X+1))/NORMTHRE(X)NX< (4X^3-9X+4+4EXP(2X))/NORMTHRE(X)NY -2EXP(X)(2X^3+3X^2-X-7)/NORMTHRE(X)NZ -(2X^2+X-4)/NORMONE(X) # BX8(2X-3)/NORMONE(X))\7)\7BY2EXP(X)/NORMONE(X)BZ(2X-3)/NORMTWO(X)XPX4 (2X^2+X-4)/NORMTWO(X)XPY -2EXP(X)*(2X^2+X-4)/(NORMONE(X)*NORMTWO(X))YPX2EXP(X)*(2X-3)/(NORMONE(X)*NORMTWO(X))YPY0-( (2X^2+X-4)^2 + (2X-3)^2 )/(NORMONE(X)*NORMTWO(X))pgsYPZProject 2: Problem 4 Space Curvep/sqrt(4e^2p+4(p+1)^2e^2p+(pL*HZ$@hW@Times New Roman<Unit Binormal Vector is BluerveRdNOn}@6́@@j@}TY@Times New RomanUnit Tangent Vector is Red(&Z d\hin}@P $@ GX(@PQ?Times New RomanUnit Normal Vector is Purple&&e`N?z.=ƌ 2#@X@W״?koTz?Times New RomandCenter of Curvature is BlacklOlH $X @@ k41?@`?Times New RomanAnimate on a to Move on the TrajectoryXP(2((A)))))8(((A)))+^h@_̵S{Q@zl@Times New RomanOsculating Circle is Fuchsiarajectory(A)))+1))^2)+2)+(2((`hU@ ^ŵ@fVY?YV?Times New Romanx = 2e^t; y = 2te^t; z = t^2-t+30OP* @@ Rf@D(x,y,z) = (2e^a,2ae^a,a^2-a+3)* @d@@}審