文档介绍：电大微积分初步考试小抄一、填空题⒈函数1的定义域是f(x)5x(-∞,5).5-x>0→x<5⒉(f(x)dx)f(x)或d(f(x)dx)f(x),y(0)1的特解为y=(0)=1(x=0,y=1)0clnyxc1e,c0方程y11(x1)y1x122214.(sinx)dxsinx+(y)(x)xln(x的定义域是(2,3)U(3,∞)2)>>20limsinx1,x时,(x)14x2的定义域是xxxln(x2)xx2⒊已知f(x)2(x).-2,-1-1,2,则f=2(ln2)⒋若f(x)dxF(x)c,则21F(2x3)-2x2f(2x3)dxx2>0x>-22ln(x2)0ln(x2)ln1⒌微分方程xy(y)4sinxexy的阶数是三2<x22<x2阶.∵(x)1的定义域是(-2,-1)U(-1,x21x1ln(x2)(x)xsin1,x0,在x0处连∞)xx2>0,lnx20x>-2,ln(x2)ln1x>-2,x21k,x0∴x|x>-2且-1续,(x)f(x0)(f(x)在x0处连续)∵(0)klimsin2xlimsin2x1limsin2x2:12lim(xsin3lim31x0xx011x02x1)xsin2x22x0xx0x(=x(x–1)(x–2)(x–3),则y(0)=-6x有界函数)y=x(x-1)(x-2)(x-3)=(x2-x)(x2-5x+6)=x4-5x3+6x2-x3+(1,1)处的切线方程是x2-6x=x4-6x3+11x2-6x,y43182226(把11xx20带入X)y(0)6,211112yxxx2y|,y2k切dxexdx2x2ln(x2)0ln(x2)nx>2x|x>,(x)(3)=27+27ln33x2xf(x)3ln3f(3)2727ln3dex2=ex2+(y)34xy(4)y7sinx的阶数为四阶二、单项选择题⒈设函数yexex,则该函数是(偶函数).∵2exexf(x)所以是偶函数⒉函数f(x)2x3的间断点是(x1,x2)分母无f(x)3xx22意义的点是间断点∴x23x20,x1,x2⒊下列结论中(f(x)在xx0处不连续,则一定在x0处不可导),伹连续并一定可导;极值点可能在驻点上,也可能在使导数无意义的点上1 1⒋如果等式 f(x)exdx ex c,则f(x)()x2(dyxyy)1111解:令u=xx2x2,u′=2x2f(x)dxF(x)C,F(x)f(x),11,yeu(ex),令ux1(eu)1)eu(x1)(ex)(1xu2exe(x)2x11ex1f(x)exf(x)x2x2⒌下列微分方程中,(yyyxsinx)是线性微分方程.(ln(x1x2))(2)时,函数f(x)ex1,x0在x0k,(2,2)是(先单调下降再单调上升),通过点(1,4)的曲线为(y=x2+3).,y(0)1的特解为(yex).三、计算题∴du1xdx2∴sinu·2du=2sinudu=2(-cos)+c=-2cosxc⒋计算定积分1xxx0u=x,v′=ex,v=ex111∴uv′dx=uv|0-0uvdx01xx11x0xedxxe|00edxx1x1xe|0e|,则该函数是(奇函数).⒈,x0)(x1)(2)时,函数f(x)(x1(x2)k,在解:limx2limx0x2x2(x2)4x0处连续.(,)上单调减少的是⒉设ye2xxx,-2x12x3(3x).解:(3xdx),u=-2x(dy1(u)′·(-2x)xyy)y1′=eu·(-2)dxx2=-2·e-(x1)1,则f(x)(x(x2))-2x31lim∴y′=-(x)在点x0处可导,则(f(x)A,2xxx01·e-2x+3但Af(x))是错误的.∴dy=(-