文科高等数学-周明儒-高数二版习题答案与提

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1、+)&%-(',*1.13.(1)y=sinu,u=cosx;(2)y=lnu,u=cosv,v=x2+1;(3)y=eu,u=2x2+1.,*1.21.(1)(2);}p1;(3);}p0;(4)2.nn+1[$!W{(−1)}{(−1)}3.!)(FY4.(1)2113(2)2.5.2.6.(1)xf(0−0)=1=f(0+0).(2)xf(0−0)=−1,f(0+0)=1.7.(1)−1;(2)4;(3)0;(4)√1.8.3.52x,

2、*1.3√22242−1−12110vx;;;1;e;e;e;e3;1;.3323,*1.41.(1)(4)S(2)(3)S2.(1)[2,+∞);(2)

3、x

4、>3,8(−∞,−3)∪(3,∞);(3)(−∞,1)∪(1,∞);(4)(0,1)∪[1,+∞).3.(1)9;(2)π;(3)cos1;(4)1.295.xa[0,2]jWg(x)=e−2−x.,*2.11.2x;2.02′83;3.S_f(0)=110−84.x3S5.(1)24x;(2)27.6

5、.^pGrpm7Xp
t#6p&Grp=-#7Xp
=t#,*2.2341−3xx11.(1)4x+x3+2x.(2)cosx+sinx.(3)(2ln2)lnx+2.3x231+sin2x3(4)secxtanx+secx,83,82secx−secx.cosx(5)4x.(6)exsinx−excosx.(7)2.(1−x2)2sin2x1+4x22−12x2x(8)−x(2−x)2.(9)1+x2.(10)√4.1−qx(11)(lnx)x[ln

6、(lnx)+1].(12)1−x−x21−x.lnx1−x21+x2.(2,2);(3,17)416,*2.32.(1){Wx1=x2;gx16=x2,+lx104x<0.13.′lf(x)=arctanx+arccotx,Wf(x),4f(0).,*2.41.1,x2;α;0;+∞0;2;e;+∞.2.(1)(−∞,0)4(2,+∞)xa(0,2)xBa;x=0,;7;;~x=2

7、,;~3.(2);x=0,;x−1.(−∞,0)xa(0,+∞)xBa3.(1)$13,$~4.(2)$ln5,$~0.4.12315A~*x6a,Vmax=27a.5.2+π.2,*2.51.2;2.200t;3.2t;4.η(8)=−1,2gD?10%,
`jn5%,"qfzD5.5%.η(16)=−1,gD?1%,
`jn1%,"qfzD0.01%.η(48)=−3,gD?1%,
`jn3%,"qfjn1.97%.,*2.61.(1)(6x+1)dx

8、;(2)−x(1−x2)−1/2dx;(3)1dx;(4)[cos(sinx)]cosxdx.xlnx112.(1)nlf(x)=(1+x)(2)lf(x)=1+x.3.,x1.4;9.9866;1.025;−0.01.4.33b30.301m;
s30m.5.b2.01π;
s2π.,*3.1143252.(1)2x2+x2+x2+c.(2)3(x−arctanx)+c.35(3)tanx−x+c.(4)x−ex+c.(5)1(x+sinx)+c.2(6)8x−312x+318x−27x+c.

9、ln8ln12ln18ln27,*3.216111.(3x−2)+c.2.−(1−2x)2+c.3.ln

10、sin(2x+1)

11、+c.1824.−1ln

12、3−2u2

13、+c.5.sinx−1sin3x+c.6.1(arctanx)2+c.43211137.2(1+lnx)2+c.8.2x2+(lnx)+c.q39.ln

14、x+1+(x+1)2+1

15、+c.√√√10.Vt=x,2(x−ln

16、x+1

17、)+c.√√2x2+111.Vx=tant,ln

18、x+1+x

19、−+c.x√111612.Vt=x,2x2−3x3+

20、6x6+c.,*3.31.(1)−xcosx+sinx+c.(2)1x3lnx−1x3+c.√39(3)xarcsinx+1−x2+c.(4)xln(1+x2)−2x+2arctanx+c.√√√√(5)−x2e−x+c.(6)Vu=x,2xsinx+2cosx+c.2,*3.41.+;−;−;+.2.bbRRRR3.2lnxdx>2(lnx)2dx;4lnxdx<4(lnx)2dx.11