; TeX output 1997.02.20:0043y? K`y cmr1018.01UUPracticeExam1J81.W(5UUpGointseach)Findthederivqativeofeachofthefollowingfunctions:[8(a)m b> cmmi10f(x)=x^ٓRcmr77S+87x;Z(b)mf(x)=x=(x^4S+81);[(c)mf(x)=3x^3|s(x^3S+83)^3;Z(d)mf(x)=xsinnx;^r[(e)mf(x)=e^ 0ercmmi7xrZcmr53;\c(f)mf(x)=cos*(e^xAIJ+8x^1=3 ʲ);[8(g)mf(x)= !", cmsy10p ofelnUUxr4S+84&;Z(h)mf(x)=x8+ln 7(x^2S+1);]q(i)mf(x)=2^x;]*(j)mf(x)=cos*(xeH O!cmsy7pɟHW Ax ).J82.W(5~pGointseach)Evqaluatethefollowinglimits(orexplainwhythelimit WdoGesUUnotexist):g[8(a)nMXlim-mx!1<$?x^2S81\wfe#3 (֍(x81)r2ز;卍Z(b)nMXlim-mx!0<$\(x81)sinnx\wfe4 (֍)x.J83.W(10pGoints)Usethede nitionofthederivqativeto ndf^0Ȳ(1)iff(x)=1=x.J84.W(10UUpGoints)Anob8jectmovingonastraightlinehaspGositions=t^3S8t^2|s.[8(a)mFindUUtheveloGcityUUv.andaccelerationa.Z(b)mWhichdirection(pGositive,&negativeorneither)istheob8jectmoving mwhenUUt=1?J85.W(10UUpGoints)Considerthefunctionf(x)=03g p wfe3荵xs.[8(a)mIsUUf(x)continuousUUatx=0?Z(b)mIsUUf(x)di erentiableatx=0? mIfUUso,then ndthevqalueofthederivative.mIfnot, thenstatewhetherthegraphhasatangentlineatthepGointm(0;0).J86.W(10pGoints)Findtheslopeofthetangentlinetothegraphofy[ٟ^2+ݷ2xy"=e^xWatUUthepGoint(0;1).*;y !", cmsy10 O!cmsy7 b> cmmi10 0ercmmi7K`y cmr10ٓRcmr7Zcmr5