Question: Question1 Findthedomainofthevectorfunctionr(t)= . Question2 Doesthelimit lim t0 exist?Ifso,findit. Question3 Atwhatpoint(s)doesthecurver(t)= intersect thespherex2+(y+1)2+(z1)2=2? Question4 Anairplane'spositionvectorattimetisdescribedbythevectorfunction r1(t)= . Aflyingsaucer'spositionvectorattimetis describedbythevectorfunctionr2(t)= . (a).Dotheairplaneandtheflyingsaucercollide?Thatis,aretheyeverinthe samespotatthesametime? (b).Dothepathsoftheairplaneandtheflyingsaucerintersect?Thatis,arethey everinthesamespotatpossiblydifferenttimes? Question5 Findavectorfunctionthatrepresentsthecurveofintersectionoftheparabolic

Question1 Findthedomainofthevectorfunctionr(t)=. Question2 Doesthelimit lim t0 exist?Ifso,findit. Question3 Atwhatpoint(s)doesthecurver(t)=intersect thespherex2+(y+1)2+(z1)2=2? Question4 Anairplane'spositionvectorattimetisdescribedbythevectorfunction r1(t)=. Aflyingsaucer'spositionvectorattimetis describedbythevectorfunctionr2(t)=. (a).Dotheairplaneandtheflyingsaucercollide?Thatis,aretheyeverinthe samespotatthesametime? (b).Dothepathsoftheairplaneandtheflyingsaucerintersect?Thatis,arethey everinthesamespotatpossiblydifferenttimes? Question5 Findavectorfunctionthatrepresentsthecurveofintersectionoftheparabolic cylindery=1z2andtheellipticparaboloidx=y2+2z2. Question6 Letr(t)=<6sin(t),8sin(t),10cos(t)>.Findanequationforaspherethatthis curvelieson. Question7 Letv(t)=<1 t,2t,3sin(3t)>. (a).Findanequation(vectororparametric)forthetangentlinetothiscurveat t=1. (b).Findanantiderivativer(t)tov(t)suchthatr(0)=<0,1,3>. 1

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