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???H ;@@ti@lۣte @v5@p*5@033333??@^ߛOw?HzG???vhsH@@@?@ @@@?@@?@?@?@F2`@xGFڻ@ k@@02??@$$$??xpD?pX^%쟧@@t@@??? exq~rP *?|to2e^t2te^tt^2-t+3!x = 2e^t; y = 2te^t; z = t^2-t+3Z' '2e^p,2pe^p,p^52??@$$$M???mgʵ?B_XuE@63?~#XuE@???mg?B_XuE@tl W}h߱D, L8@2e^a2ae^aa^2-a+3(x,y,z) = (2e^a,2ae^a,a^2-a+3)-p+3) to (2e^p+(-e^(42???$$$??NWp2`&?ڷ>u@???`#?XÑԕ~t/ 2e^a2ae^aa^2-a+3 2e^a+TX(a)Cseg (2e^a,2ae^a,a^2-a+3) to (2e^a+TX(a),2ae^a+TY(a),a^2-a+3+TZ(a)) 2ae^a+TY(a)a^2-a+3+TZ(a)p)*(p+1)+2p^2-2p+.7542???$$$??NWp2`&?ڷ>u@???`#? aϑۑpHt4ĩzd2e^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???$$$??NWp2`&?ڷ>u@???`#?<@ðTN2e^a2ae^aa^2-a+3 2e^a+BX(a)Cseg (2e^a,2ae^a,a^2-a+3) to (2e^a+BX(a),2ae^a+BY(a),a^2-a+3+BZ(a)) 2ae^a+BY(a)a^2-a+3+BZ(a)?0!j42???$$$??ݦS?xٹxZ0[@`@`#z? @9 @???<$8LXn(b8ֵ2e^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???$$$:eV???஖@0R众?@Z @஖@0R?@Z @???஖@0R伷?@Z @VpMX:p|ÒΒ3T\2exp(a) + RHO(a)*Nx(a)2*a*exp(a)+RHO(a)*Ny(a)a^2-a+3 +RHO(a)*Nz(a)Q(x,y,z) = (2exp(a) + RHO(a)*Nx(a),2*a*exp(a)+RHO(a)*Ny(a),a^2-a+3 +RHO(a)*Nz(a))5O02??h!@$$$Xy@?S;s-?PiI棁@Q@~"@ȋzF@???ڒl$4Z˶PPX;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) )_ xyz=Y;ݻHXT@ QPy@@?@@@@@@@@@@@@@@?@@@@@@@@@@ @ @ @SQRT( 4EXP(2X)(X^2+2X+2) + (2X-1)^2 )ۺeLXNORMZEROdͰ SQRT( (2X^2+X-4)^2 + (2X-3)^2 +4EXP(2X) )NORMONEͰSQRT( (2X-3)^2 +(2X^2+X-4)^2 )NORMTWOű(4X^2-8X+3-4EXP(2X)*(X+1))^2 reenMAPƱ(4X^3-9X+4+4EXP(2X))^2 +8)^2+(4P-6)^2+16E^(2P))))MBƱ4EXP(2X)*(2X^3+3X^2-X-7)^2 42*MCSQRT(MA(X) + MB(X) +MC(X) )NORMTHRET 0.5EXP(-X)*NORMZERO(X)^3/NORMONE(X)1#&P&RHO2EXP(X)/NORMZERO(X)TX2EXP(X)(X+1)/NORMZERO(X)TYP(2X-1)/NORMZERO(X)TZ(4X^2-8X+3-4EXP(2X)*(X+1))/NORMTHRE(X)NX (4X^3-9X+4+4EXP(2X))/NORMTHRE(X)NYL -2EXP(X)(2X^3+3X^2-X-7)/NORMTHRE(X)NZ -(2X^2+X-4)/NORMONE(X) # BX(2X-3)/NORMONE(X))\7)\7BYH2EXP(X)/NORMONE(X)BZ(2X-3)/NORMTWO(X)XPX (2X^2+X-4)/NORMTWO(X)XPYD -2EXP(X)*(2X^2+X-4)/(NORMONE(X)*NORMTWO(X))YPX2EXP(X)*(2X-3)/(NORMONE(X)*NORMTWO(X))YPY-( (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+(@.2@ХJ@܇@~@Times New RomanUnit Binormal Vector is BluerveRdNO 2#@@0֨8˂@PNa1@Times New RomanUnit Tangent Vector is Red(&Z d\hi 2#@ R[B0@B+_@p=oKN@Times New RomanhUnit Normal Vector is Purple&&e`N?z.=ƌ 2#@X@`@PE(=@Times New Roman Center of Curvature is BlacklOlH $//E@}Kt@s4L?Yl?Times New RomanAnimate on a to Move on the TrajectoryXP(2((A)))))8(((A)))+^h@_̵P*@@Times New Roman·Osculating Circle is Fuchsiarajectory(A)))+1))^2)+2)+(2(( P@g0R@-_?x(?Times New Romanx = 2e^t; y = 2te^t; z = t^2-t+30OP* @g0i @H(x,y,z) = (2e^a,2ae^a,a^2-a+3)* @d@@}審xi l@seg (2e^a,2ae^a,a^2-a+3) to (2e^a+TX(a),2ae^a+TY(a),a^2-a+3+?* @sjҍ8͊@1Courier Newseg (2e^a,2ae^a,a^2-a+3) to (2e^a+NX(a),2ae^a+NY(a),a^2-a+3+* ;h)@Ts @1Courier Newpseg (2e^a,2ae^a,a^2-a+3) to (2e^a+BX(a),2ae^a+BY(a),a^2-a+3+* R⠷@HW[2>_@1Courier New(seg (2e^a,2ae^a,a^2-a+3) to (2e^a+RHO(a)*NX(a),2ae^a+RHO(a)** g@P.q.s垂@1Courier New(x,y,z) = (2exp(a) + RHO(a)*Nx(a),2*a*exp(a)+RHO(a)*Ny(a),a^* o_@gNEl@1Courier Newx = 2exp(a) + RHO(a)*( Nx(a) + xpx(a)*cos(t) + ypx(a)*sin(t)* дk@'r8 T@1Courier New