第PAGE《微積分(二)》模擬題單項(xiàng)選擇∫fxdx=x22(1-x2)2+c-2(1-x2)2+c-1/2(1-x2)2+c1/2(1-x2)2+c[答案]:C設(shè)fx=e-x-1/x+c1/x+clnx+c-lnx+c[答案]:B∫fx=x2xe2x2x2e2xXe2x(2+x)2xe2x(1+x)[答案]:D已知f'1xff1xf'x=f[答案]:C已知∫fx2dx=e11ee[答案]:B已知F(x)是sinx2的一個(gè)原函數(shù),則dF(x2)=()2xsinx4dxSinx4dx2xsinx2dxsinx2dx2[答案]:A若f'(sinxsinx-1/2sin2x+cx-1/2x2+c1/2x2-x+ccosx-sinx+c[答案]:B∫dx–cotx+tanx+ctanx+cotx+c2cot2x+c2tan2x+c[答案]:A若F'(x)=f(x),則∫dFf(x)F(x)f(x)+cF(x)+c[答案]:D下列哪個(gè)表達(dá)式等于f(x)()d(∫f(x)dx)∫df(x)(∫f(x)dx)’\∫f(x)dx[答案]:C\若f(x)的導(dǎo)函數(shù)是sinx,則f(x)有一個(gè)原函數(shù)為().1+sinx1-sinx1+cosx1-cosx[答案]:B當(dāng)被積函數(shù)含有x2-a2時(shí)asintatantasectaccost[答案]:C欲使∫λfxdx=λ∫f(x)dx,對(duì)常數(shù)λ沒(méi)有限制λ≠0λ＞0λ≤0[答案]:A設(shè)I=∫tanxdx,則()lnlnln-ln[答案]:D設(shè)I=∫lnxdx則()I=I=I=xlnx+CI=xlnx-x+C[答案]:DI=∫dxsinx,則lnlnlnln[答案]:B已知函數(shù)f(x+y,x-y)=x2-y2,則f(x,y)/x+f(x,y)/y=()2x-2y2x+2yx+yx-y[答案]:C點(diǎn)()是二元函數(shù)z=x3-y3+3x3+3y2-9x的極大值點(diǎn)(1,0)(1,2)(-3,0)(-3,2)[答案]:D函數(shù)z=1ln?(x+y≠0x+y>0x+y≠1x+y>0且x+y≠1[答案]:D設(shè)函數(shù)y=0x(t-1)dt,則極小值1/2極小值-1/2極大值1/2極大值-1/2[答案]:B若012x+kdx=2,0-111/2[答案]:C-11-220發(fā)散[答案]:D當(dāng)()時(shí),廣義積分-∞0k>0k≥0k<0k≤0[答案]:C設(shè)f(x)是連續(xù)函數(shù),F(x)是f(x)的原函數(shù),則()當(dāng)f(x)是奇函數(shù)時(shí),F(x)必是偶函數(shù)當(dāng)f(x)是偶函數(shù)時(shí),F(x)必是奇函數(shù)當(dāng)f(x)是周期函數(shù)時(shí),F(x)必是周期函數(shù)當(dāng)f(x)是單調(diào)函數(shù)時(shí),F(x)必是單調(diào)函數(shù)[答案]:A若∫fxdx=x2xe2x2x2e2xxe2x2xe2x(1+x)[答案]:D26.直線(xiàn)l1:與直線(xiàn)l2:的夾角為().A.B.C.D.[答案]:B27.下列哪一個(gè)不是sin2x的原函數(shù)().A.B.C.D.[答案]:D28.().A.B.C.D.[答案]:C29.下列級(jí)數(shù)中,發(fā)散的級(jí)數(shù)是().A.B.C.D.[答案]:D30.設(shè),則在點(diǎn)O(0,0)處().A.偏導(dǎo)數(shù)存在,函數(shù)不連續(xù)B.偏導(dǎo)數(shù)不存在,函數(shù)連續(xù)C.偏導(dǎo)數(shù)存在,函數(shù)連續(xù)D.偏導(dǎo)數(shù)不存在,函數(shù)不連續(xù)[答案]:A31.().A.B.C.D.[答案]:A32.設(shè),則有().A.極小值2-eB.極小值e-2C.極大值2-eD.極大值e-2[答案]:A32.().A.B.C.D.[答案]:D33.若,則().A.B.C.D.[答案]:A34.設(shè),則().A.B.C.D.[答案]:D35.已知F(x)是sinx2的一個(gè)原函數(shù),則dF(x2)=().A.2xsinx4dxB.sinx4dxC.2xsinx2dxD.sinx2dx2[答案]:A36.若f’(sin2x)=cos2x,則f(x)=().A.sinx-?sin2x+cB.x-?x2+cC.?x2-x+cD.cosx-sinx+c[答案]:B37.若F’(x)=f(x),則∫dF(x)=().A.F(x)B.f(x)C.f(x)+cD.F(x)+c[答案]:D38.∫dxA.-cotx+tanx+cB.tanx+cotx+cC.2cot2x+cD.2tan2x+c[答案]:A39.若∫fxdx=x2+cA.2(1-x2)2+cB.2(2-x2)dxC.-?(2-x2)2+cD.-?(1-x2)2+c[答案]:C40.初等函數(shù)y=f(x)在其定義域[a,b]上一定().A.連續(xù)B.可導(dǎo)C.可微D.不連續(xù)[答案]:A41.函數(shù)z=xy在(0,0)點(diǎn)處一定為()A.極大值B.極小值C.無(wú)法確定D.不取得極值[答案]:D42.微分方程y"-y=ex+1的一個(gè)特解應(yīng)有形式(式中a,A.aex+bB.axex+bxC.aex+bxD.axex+b[答案]:D43.二元函數(shù)z=f(x,y)在點(diǎn)(x0,y0)的偏導(dǎo)數(shù)存在,是在該點(diǎn)可微的()A.充分條件B.必要條件C.充要條件D.無(wú)關(guān)條件[答案]:B44.若f(x,y)在點(diǎn)(0,0)的兩個(gè)偏導(dǎo)數(shù)存在,則f(x,y)在點(diǎn)(0,0)()A.連續(xù)且可微B.連續(xù)但不一定可微C.可微但不一定連續(xù)D.不一定可微也不一定連續(xù)[答案]:D45.曲線(xiàn)y=2x/1-x2的漸近線(xiàn)條數(shù)為()A.0B.1C.2D.3[答案]:D46.試求limx→02-A.-1/4B.0C.1D.∞[答案]:A47.設(shè)f(x)定義域?yàn)?1,2),則f(lgx)的定義域?yàn)?)A.(0,lg2)B.(0,lg2]C.(10,100)D.(1,2)[答案]:C48.積分與()有關(guān)A.s,t,xB.s,tC.x,tD.s[答案]:D49,則k=()A.1B.2C.ln2D.1/2ln2D[答案]:C50.limx→0A.1B.2C.4D.3[答案]:C二.計(jì)算題1.求一階線(xiàn)性微分方程的通解.[答案]:解:易知,則通解為2.計(jì)算二重積分,其中D是圓環(huán)域.[答案]:解:在極坐標(biāo)下,圓環(huán)的表示為,積分區(qū)域,則3.求冪級(jí)數(shù)的收斂域,并求出它的和函數(shù)．[答案]:解:令,因?yàn)?故收斂半徑為1,收斂區(qū)間為(-1,1),在處,級(jí)數(shù)為,該級(jí)數(shù)發(fā)散,在處,級(jí)數(shù)為,該級(jí)數(shù)收斂,因此收斂域?yàn)閇-1,1).設(shè),則,又所以,即4.設(shè)為二元可微函數(shù),又假設(shè),試證明:[答案]:證明:因?yàn)?,則.5.要制造一個(gè)帶蓋的長(zhǎng)方體水槽,已知它的底部和頂部造價(jià)為每平方米18元,側(cè)面造價(jià)為每平方米6元,設(shè)計(jì)的總造價(jià)為216元,問(wèn)如何選