; TeX output 1997.03.13:2028y? K`y cmr1018.01UUPracticeExam2J81.WRecallʴthatthevolumeofa(rightcircular)coneis b> cmmi10VÚ= ٓRcmr71&fes3 폵[rG^2Ðh, wherer WisItheradiusofthebase,andhistheheight.jSuppGosethatthedistanceWfromUUthetiptothebase'srimis1unit.[8(a)m(12UUpGoints)ShowthatV= K1K&fes3 )[ٲ(h8 !", cmsy10h^3|s),UUwherehisbGetween0and1.Z(b)m(18UUpGoints)Determinethemaximumvolumeofsuchacone.J82.W(243pGoints)Sketchthegraphoff(x)=x^2<+ɵx^ O!cmsy71 t.aIndicate3theintervqals Wwherethefunctionisincreasing,decreasing,concaveuporconcavedown.WLabGelUUallrelativemaximaandminimaandin ectionpoints.J83.W(12wpGoints)Anelasticbandoflengthxand(circularcross-sections)ofWradiusQ r(isbGeingstretchedattherateof1cm/sec.pYAssumingthevolumeWremains=constant,$atwhatrateistheradiusshrinkingwhenxۙ=10=cmWandUUr5=0:1cm.mg>>PSfile=prac-exam2-fig.eps llx=0 lly=0 urx=542 ury=147 rwi=3982J84.W(6UUpGoints)StatetheMeanV*alueTheorem.J85.WApproximateUUPp Pfe E4:04 !by[8(a)m(8ޏpGoints)applyingoneiterationofNewton'smethodtothefunctionmf(x)=x^2S84:04;Z(b)m(8UUpGoints)usingalinearapproximationofp fe3荵xatx=4.J86.WEvqaluateUUthefollowinglimits(orexplainwhythelimitdoGesnotexist):g[8(a)m(6UUpGoints)lim- 0ercmmi7x!0<$le^2x >781lwfe7 (֍sinqx6ֲ;Z(b)m(6UUpGoints)limx!1zx1=x ;.*;yͲ} !", cmsy10 O!cmsy7 b> cmmi10 0ercmmi7K`y cmr10ٓRcmr7 [