1、Review0000,0,1,0,0.0一b.00Example30arcsinlim(arcsin)xxxxtan30limxxxeexExample10limxxex1txLHospitals Rule301tan1 sinlimxxxxExample1212312()2.lim(12)xtxtf u du dtxWhere is differentiable and f1212lim()0,lim()1000.xxf xfxd.Example2220limxtxxt e dtxe3sinlim32cosxxxxxe.1lim()xxxexExample2lim()xxxx111lim()
2、ln1xxxlim(ln)xxxlnlimxxxxlim(ln(1)xxexExample21limln(1)xxxxlim()xxxxxf.0Example22lim(arctan2)2xxxg.exxx )11(lim13101tanlim()1 sinxxxxExample210arcsinlim()xxxx112012lim()(0)xxxnxxnaaana aah.000lim(tan2)xxxExamplei.001lim(ln)xxxExamplexxx)11(lim01222201111lim()12ndxxnnnnnnl.ExampleExample Find a,b,suc
3、h that0)1(lim33bxaxx0)1(lim313xbxxa0)1(lim33bxaxx机动 目录 上页 下页 返回 结束 SolutionSincethus01lim33xbxaxx331xy,01a,1a)1(lim33xxbx2333231)1(1limxxxxx0 xy机动 目录 上页 下页 返回 结束 thereforeThe Mean Value Theorem2.Show that for bbabaabaln.0ab.)(xf,0 a),0(a0)(afRc),0(a0)()(cf ccRfLetbe continuous on,differentiable on.I
4、f,then for every realthere is at least one numberinfor which1.20()2()()limhf ahf af ahhExampleIf is continuous,find f)(xf,ba),(ba)(0)(bfaf,0)(cfc),(ba.0)(cfLetbe continuous onexists on.If,andShow that there is at least one numberinfor which)(xf cin),(ba3.4.Show that for 5.Show that for.0 x10,0,0cxcx
5、cx)(exexApplications of differentiationSketch the graph ofExample323)(xxxfOptimization ProblemsExamplenpnp15.010 nn330A manufacturing plant has a capacity of 30 articles per week.Experience has shown that articles per week can be sold at a price of dollars each whereand the cost of producingarticles
6、 isdollars.How many articles should be madeeach week to give the largest profit?Integrals1.Show thatExample24711171214dxxP435,5,6,15,10,17Integrals1.Find if )(xfxxdttfexf02)()(0d|xy(0)y20()dxxxyytte2、Find andifxtxdttxx3313)31(3lim.31.=_.Fill in the blanks:20022limxdtexttx2.badttfdxd)(=_.3.If,then=_.
7、dxxxf)(lnxexf)(1222201111lim()12ndxxnnnnnnIntegrals1.The Substitution Ruledxex11Exampledxeexx2111xxxxxd)1(arcsin1IntegralsExampledxeeexxx21)1(22arctand(1)xxxxdxx22ExampleLet R be the region bounded by the curve,xeyand the lines.0,0 xy(1)Evaluate the area of the region R(2)Find the volume of the solid generated by revolving the R about the x-axis.
