高等数学基础题库

题）CA轴轴设在（C若（BDC轴轴当DB11dxd()arctanxdxd()(A)(B)1xx22xd(22)2dxd(tan)cotdxx(D)x(C)xxACBA轴轴B若（CDB，，，，C轴轴BCD当CA设（B设在（D设（A设（D若C若若若当CD在在在在DDAC设在在35.设在B（A若（DD若（B（D若（B和和所CD．B．．．设．（．．．D内.．在..．在.（．C．．．当（01．．D.．.．.在.在A．．．．．．D．D．（A．．．．BD．．．．（C．．．．B．．．．fx(C0fxfx00．fx0DxD．．y=x+3Dy=x+422．C．．．0（B1B．．D．在．在A．．．．设（DB（D若cosx（BcosxsinxBD］．A．C；xCyB．（B||．．．x(x)f．Cln(x2)()．()．(()．()x02x(x)当k（fx0.Bk,x02101C．．D(x)f(x)0.f(x)xx.．f在x00.(x)xx.．f在x00Adf(x)dxf(x)(x)dxf(x)．f．．dxdf(x)dxf(x)df(x)f(x)．=(AB10．∞设．在.A．．．.DC01．.A01C．CD01C．.C2在.BB当．x.C(A....设在在）.A在.AD12．.BBxxy在ex1y.Ax-1）．．-+）．(x)2x9x12x3f32.D．(．[2,)．yyx3，.B2x3x12x1432.D．11,20）B．22(x)(x4)(xfB2231x1．x．．(x)(x4)(xfA31x1．x．．(x)(,)在[f(x]d设f（.B(x)f(x)f(x)Cf(x)f11x（.B201．．）(x)(x)()2gxx，Nf(x)x()Y2gxx，ff(x)(,)f(x)f(x)f(x)f(x)yY(x)(,)fNxxyyyy.Yx)2.Nx.Nx20.Ysinxlim.Yxx.Nsinx当x0Nx1sin当xx0Yx(x)(x)f(x)x.Nffx00fxlim()()fxf(x)x.Yx000xx0x293.Yx(x)x)x)fx3x29x3f(x)，.Nx(xxx()x2fxff2.Y(xxx()1.Nfxx21x),x0(x)ke.Yx0fx,xk0x1x),x0(x)x0kNfx,x0xk11)ee.Yx22xxx1,x00.Yyxsinx,x0limf(x)A()xxfxA.Y若若0xx0limf(x)A()xxfxA.N0xx0f(x)f(x)设f0limlimf.Yxxx0x0f(x)f(x)f0limlimf(x).N设设xxx0x0f(x)f(x)f0limlimNxxx0x0f(x2h)f(x)(x)limf(x).Y设f设f设f在x002h00h0f(x2h)f(x)(x)lim2()在xfx.N002h00h0fx)fxe(x)elim.Yxx0fx)fx(x)elimN设fxx0(x)x(xx2)(x(x)x(xx2)(xf99!f设f设f若f若f若f.Y99.N(x)(x)(x)xxN00xxN00xxY00(x)(x)(x)若f若f若fxxN00xxY00xxY001sin,x0x2(x)(x)ffxffY0,x01sin,x0x2xN.Y0,x0dfx)2ln5x(e)e设f2xxxxdxxdfx)dx(e)e设f2.Nxx1(x)x1在ff.Y2π(x)x(,1)在y1.Y4π(x)x(,1)在f.N4xylnx)x设y设y2x2.Yx1xxxxy.Yx设y.Y(x)满足在[a,](a,b)内可导，则存在(a,b)fY(x)(a,b)(a,b)fN(2,)2f(x)=3x+4x1.N.Y2f(x)=3x+4x1，(2,)2f(x)=3x+4x1.(2,)2f(x)=3x+4x1.(x)(x)f(x)0f(x)0f(x)f(x)ff.Y.N(x)(a,b)在(a,b)f(x)0,f(x)0设fx000f(x)在xY0(x)(a,b)在(a,b)f(x)0,f(x)0设fx000f(x)在xN0(x)(a,b)在f(x)0,f(x)0f(x)f(x)0,f(x)0f(x)f(x)0,f(x)0f(x)f(x)0,f(x)0f(x)设fY(x)(a,b)在设fN(x)(a,b)在设fN(x)(a,b)在设fN(x)(a,b)在x(a,b)，f(x)0f(x)0f(x)0xxxxxx设fx时时时，，00000(x)则x是fY0(x)(a,b)在x(a,b)，f(x)0时设fx0(x)则x是fN0(x)f(x)f(x)f(x)()fffxx是fxYY000(x)(x)xx是．N．N00xx是00x)y2x)yff2NY(x)e2(x)e2N(x)[a,]在f(x)0f(x)[a,]f(a)f(a)ff在f(x)[a,]在YN(x)[a,]在f(x)0ff(x)25x3x3，Y(x)25x3x3，Nfx()22aa，bYaxbx32()fxaxbx，bN32(x)(x)f(x)f(x)若fYN若f()d()fxxfx.N()d()fxxfx+C.Ydf(x)dxf(x).Ydf(x)dxf(x).Ndf(x)dxf(x).Ydxf(x)x(x)x(xxcosxcY若f若fdf(xxsinxc.N(x)dx()2xx22f3xfx3.Ydxd1f(x)dxf(x).N33dx31(x)dxF(x)cfxxFxc.Y()d2()若fx11若f(x)dxF(x)c(x)dxF(x)c.Nfxx由区间[a,]yf(x)yg(x)和xa和xb所bf(x)g(x)dx．Ya由区间[a,]yf(x)yg(x)和xa和xb所[f(