高等数学( 北大版)答案一习题1.2

1习题1.222222222151ln(4);(2)ln;(3)ln;(4).1425340,||4,||2,(,2)(2,).10101(2)0..11,(1,1).101015(3)1,540.540,(4xxxyxyyyxxxxxxDxxxxDxxxxxxxxxx求下列函数的定义域或1.:(1)解(1)1221221)(4)0,1,4.(1,4).(4)2530.(21)(3)0,3,1/2.(,3)(1/2,).(),()1,(0,3).()(1,10).(2)()ln(1sin),(/2,],()(,ln2].(3)(xxxDxxxxxxDfXXfxxXfXfxxXfXfx求下列函数的值域其中为题中指定的定义域2..(1)222122)32,[1,3],320,230,(1)(3)0,1,3,()[0,(1)][0,4].(4)()sincos,(,).()2(sincos(/4)cossin(/3))2sin(/4),()[2,2].ln(1)(),(1)ln10xxXxxxxxxxxfXffxxxXfxxxxfXxfxf求函数值：设求3.2,(0.001),(100);(2)()arcsin,(0),(1),(1);1ln(1),0,(3)()(3),(0),(5).,0,cos,01,(4)()1/2,1,(0),(1),(3/2),(2).2,13(1)()lxffxfxfffxxxfxfffxxxxfxxffffxfx设求设求设求解264og,(1)log10,(0.001)log(10)6,(100)log10(2)(0)0,(1)arcsin(1/2)/6,(1)arcsin(1/2)/6.(3)(3)ln4,(0)0,(5)5.(4)(0)cos01,(1)1/2,(3/2)22,(2)4.24.(),2xfffffffffffffxfxxx=4.设函数112,(),(1),()1,,.()2213(),2;(1),1,3,2211fxfxfxfxfxxxxfxxfxxxxxx求解2333322332224121/21()11,2;,0,1/2,2221/2112,2.()2()()(),()()()3333.6.()lxxxfxxfxxxxxxxxxfxxfxxfxfxxxxfxxfxxxxxxxxxxxxxxxxxfx设求，其中为一个不等于零的量.设解5.224222n,0,(),,(()),(()),(()),(()).(())(ln)lnln,1;(())(),;(())()ln,0;(())(ln)ln,0.0,0,,0;7.()(),0;1xxgxxxffxggxfgxgfxffxfxxxggxgxxxfgxfxxxgfxgxxxxxxfxgxxx试求设解(()),(()).,0,,()0,(())0.(0),0,0,0,(())(),0.,0.8.:(1)[],[];(2)[];1(3)sinh()();21(4)cosh()(2xxxxfgxgfxxxxgxfgxgxxgfxgxxxxyxxxyxxyxeexyxee求作下列函数的略图其中为不超过的最大整数解2);,00,(5)1,10.xxxyxx3（1）（2）（3）（4）（5）2242222,0,9.():,0,(1)();(2)|()|;(3)();(4)(||).(1),.,0,(2)|()|,0.,0,,0,(3)(),0,0.(4)(||),xxfxxxyfxyfxyfxyfxyxxxxyfxxxxxxxyfxxxxxyfxx设求下列函数并且作它们的图形解.x4222222210.:2(1)(0);2(2)sinh();(3)cosh(0).2(1),240,4,4().2(2),,210,1,ln(1),2ln(1),().(3xxxxxyxxyxxyxxxyxyxxyyyxxxxeeyzezyzezyyxyyyxxx求下列函数的反函数解222222222222222),,210,1,ln(1),2ln(1),(1).11.coshsinh1.(2)(2)coshsinh1.22412.?(1),(xxxxxxxxxxxxxeeyzezyzezyyxyyyxxxxxeeeeeeeexxyex证明下列函数在指定区间内是否是有界函数证2210,);(2)(0,10);(3)ln,(0,1);(4)ln,(,1),0.1(5)cos(2),(,);||12.2sin21xxxyexyxxyxxrreyxyx否是否其中是是5221010(6)sin,(,);.(7)cos,(10,10).yxxxyxxx否是6426642642666613.1(1,)(1)(1)111(1).112113.(,).13||13,||1,3,11||3,(,).yxxxxxxyxxxxxxxxxxyxxxxxxxxxxxxxyyx证明函数在内是有界函数.研究函数在内是否有界时,时证解