大学高数英文版练习题-学生

Test4Date___________Class___________Name___________Score__________IfyouhavefoundanymistakesinTest4,pleasereportthemtoyourMathteacher!1.Choosethebestanswerforeachquestion.(4*15=60pts.)(1)Ifsatisfies:(1)fiscontinuouson[a,b];:[,],fabR(2)fisdifferentiableon(a,b);(3)f(a)=f(b),thenthereexistsatleastonepointsuchthat（）.(,)ab()f(A)(B)(C)(D)01()()ffa1(2)Ifsatisfies:(1)fiscontinuouson[a,b];:[,],fabR(2)fisdifferentiableon(a,b);thenthereexistsatleastonepointsuchthat（）.(,)ab()f(A)(B)()()()baffbfa()()()ffbfa(C)(D)()()()fbfafba()()()ffafb(3)Ifx0,then（）.(A)(B)(C)(D)xeex1xex)1(xeexxx)1ln((4)If,thenintheopeninterval（）.21xxy)1,1(（A）yisincreasing（B）yhasarelativemaximum（C）yisdecreasing（D）yhasarelativeminmum(5)If,thenat（）.()xfxxe1x（A）fisincreasing（B）fhasarelativemaximum（C）fisdecreasing（D）fhasarelativeminmum(6)Letcontinuous，and=0，=1，thenis（）valueof.()fx(0)f0lim()xfx(0)f()fx(A)localmaxima(B)localminima(C)notlocalextreme(D)maybelocalextreme(7)（）initsdomain.1123xxy（A）isincreasing（B）isdecreasing（C）isconcave（D）isconvex(8)Ifobtainlocalmaximumat，thenitmustbe（）.)(xfy0xx（A）（B）0)(0xf0)(0xf（C）且（D）=0或不存在0()0fx0)(0xf)(0xf0()fx(9)（）()lnfxxx（A）isdecreasingin（B）isdecreasingin1(0,)e1(),e1Test4Date___________Class___________Name___________Score__________IfyouhavefoundanymistakesinTest4,pleasereportthemtoyourMathteacher!（C）isdecreasingin(o,+)(D)isincreasingin（0,+）(10)Ifin,,thenis（）in.(,)ab()0fx()0fx)(xfy(,)ab（A）decreasingandconvexup（B）decreasingandconvexdown（C）increasingandconvexup（D）increasingandconvexdown(11)Whatareallvaluesofxforwhichthefunctionfdefinesbyisincreasing?().32()397fxxxx（A）（B）（C）or（D）or31x11x3x1x1x3x(12)Iffisthefunctiondefinedby,whatareallthex–coordinates54()35fxxxofpointsofinflectionforthegraphoff?().（A）（B）and1（C）（D）,0,and11011(13)Ifisstrictlyincreasingin，thenshouldbesatisfied（）.baxy2),0(ba,（A）（B）（C）（D）0,0ba0,abR0,0ba0,abR(14)2isthe（）foron.32362yxxx[1,1]（A）localmaximum（B）localminimum（C）globalmaximum（D）globalminimum(15)Whichofthefollowingcurveshastheinflectionpoint(0,0)?（）.（A）（B）（C）（D）2yx3yx4yx23yx2.FindtheLocalmaximumandminimumfor7186223xxxy.(10pts.)3.Findtheintervalsofconcavityandconvexityandtheinflectionpointsfor.(10pts.)xxey4.Provethefollowinginequalities:(2*10=20pts.)(1)tanxxif(2).0,.2xxx1211(0)x2