電大微積分初步考試小抄最新完整版小抄

電大微積分初步考試小抄一、填空題⒈函數(shù)SKIPIF1<0的定義域是（－∞，5）．5－SKIPIF1<0＞0→SKIPIF1<0＜5⒉SKIPIF1<01．SKIPIF1<0，SKIPIF1<0⒊已知SKIPIF1<0，則SKIPIF1<0=SKIPIF1<0．⒋若SKIPIF1<0，則SKIPIF1<0SKIPIF1<0．⒌微分方程SKIPIF1<0的階數(shù)是三階．∵SKIPIF1<06.函數(shù)SKIPIF1<0的定義域是（-2，-1）U（-1，∞)SKIPIF1<0∴SKIPIF1<07.SKIPIF1<02．SKIPIF1<0SKIPIF1<08.若y=x(x–1)(x–2)(x–3)，則SKIPIF1<0(0)=-6y=x(x-1)(x-2)(x-3)=(x2-x)(x2-5x+6)=x4-5x3+6x2-x3+5x2-6x=x4-6x3+11x2-6x,SKIPIF1<0SKIPIF1<0（把0帶入X）SKIPIF1<09.SKIPIF1<0SKIPIF1<0SKIPIF1<0或SKIPIF1<010.微分方程SKIPIF1<0的特解為y=ex.SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0又y(0)=1(x=0,y=1)SKIPIF1<0SKIPIF1<011.函數(shù)SKIPIF1<0的定義域是SKIPIF1<0SKIPIF1<012.若函數(shù)SKIPIF1<0,在SKIPIF1<0處連續(xù)，則SKIPIF1<01．SKIPIF1<0(SKIPIF1<0在SKIPIF1<0處連續(xù))∵SKIPIF1<0SKIPIF1<0（無窮小量x有界函數(shù)）13.曲線SKIPIF1<0在點SKIPIF1<0處的切線方程是SKIPIF1<0SKIPIF1<0，SKIPIF1<0SKIPIF1<0SKIPIF1<014.SKIPIF1<0sinx+c 15.微分方程SKIPIF1<0的階數(shù)為三階16.函數(shù)SKIPIF1<0的定義域是（2,3）U（3，∞）SKIPIF1<017.SKIPIF1<01/218.已知SKIPIF1<0，則SKIPIF1<0=27+27ln3SKIPIF1<0SKIPIF1<019.SKIPIF1<0=ex2+c20.微分方程SKIPIF1<0的階數(shù)為四階二、單項選擇題⒈設(shè)函數(shù)SKIPIF1<0，則該函數(shù)是（偶函數(shù)）．∵SKIPIF1<0⒉函數(shù)SKIPIF1<0的間斷點是（SKIPIF1<0）分母無意義的點是間斷點∴SKIPIF1<0⒊下列結(jié)論中（SKIPIF1<0在SKIPIF1<0處不連續(xù)，則一定在SKIPIF1<0處不可導(dǎo)）正確．可導(dǎo)必連續(xù)，伹連續(xù)并一定可導(dǎo)；極值點可能在駐點上，也可能在使導(dǎo)數(shù)無意義的點上⒋如果等式SKIPIF1<0，則SKIPIF1<0（SKIPIF1<0）SKIPIF1<0SKIPIF1<0⒌下列微分方程中，（SKIPIF1<0 ）是線性微分方程．6.設(shè)函數(shù)SKIPIF1<0，則該函數(shù)是（奇函數(shù)）．7.當SKIPIF1<0（2）時，函數(shù)SKIPIF1<0在SKIPIF1<0處連續(xù).8.下列函數(shù)在指定區(qū)間SKIPIF1<0上單調(diào)減少的是（SKIPIF1<0）．9.以下等式正確的是（SKIPIF1<0）10.下列微分方程中為可分離變量方程的是（SKIPIF1<0）11.設(shè)SKIPIF1<0，則SKIPIF1<0（SKIPIF1<0）12.若函數(shù)f(x)在點x0處可導(dǎo)，則(SKIPIF1<0，但SKIPIF1<0)是錯誤的．13.函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0是（先減后增）14.SKIPIF1<0(SKIPIF1<0）15.下列微分方程中為可分離變量方程的是（SKIPIF1<0）16.下列函數(shù)中為奇函數(shù)是（SKIPIF1<0）17.當SKIPIF1<0（SKIPIF1<0）時，函數(shù)SKIPIF1<0在SKIPIF1<0處連續(xù).18.函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0是（先單調(diào)下降再單調(diào)上升）19.在切線斜率為2x的積分曲線族中，通過點（1,4）的曲線為（y=x2+3）．20.微分方程SKIPIF1<0的特解為（SKIPIF1<0）．三、計算題⒈計算極限SKIPIF1<0．解:SKIPIF1<0⒉設(shè)SKIPIF1<0，求SKIPIF1<0.解：SKIPIF1<0SKIPIF1<0SKIPIF1<0，u=-2xSKIPIF1<0′·(-2x)′=eu·（-2）=-2·e-2x∴y′=-2e-2x+SKIPIF1<0∴dy=(-2·e-2x+SKIPIF1<0)dx⒊計算不定積分SKIPIF1<0解：令u=SKIPIF1<0,u′=SKIPIF1<0∴SKIPIF1<0∴SKIPIF1<0·2du=SKIPIF1<0=2(-cos)+c=-2cosSKIPIF1<0⒋計算定積分SKIPIF1<0u=x，v′=ex,v=ex∴SKIPIF1<0SKIPIF1<0v′dx=uvSKIPIF1<0SKIPIF1<0∴原式=2SKIPIF1<0SKIPIF1<0SKIPIF1<0，求SKIPIF1<0解：SKIPIF1<0y1=lncosxy1=lnu1,u=cosx∴SKIPIF1<0y1=SKIPIF1<0∴dy=(SKIPIF1<0)dxSKIPIF1<0解：SKIPIF1<0令u=1-2x,u′=-2∴SKIPIF1<0SKIPIF1<0SKIPIF1<0解：u=x,SKIPIF1<0SKIPIF1<0=SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0，求SKIPIF1<0y1=sin3xy1=sinu,u=3x,SKIPIF1<0∴y′=2xln2+3cos3x∴dy=(2xln2+3cos3x)dxSKIPIF1<0SKIPIF1<0u=x,v′=cosx,v=sinxSKIPIF1<0SKIPIF1<0SKIPIF1<0令u=lnx,u′=SKIPIF1<0,du=SKIPIF1<0dx,1≤x≤e0≤lnx≤1∴SKIPIF1<0∴原式=1+5·SKIPIF1<0=SKIPIF1<0SKIPIF1<0解：SKIPIF1<0SKIPIF1<0，求SKIPIF1<0解：SKIPIF1<0(SKIPIF1<0),SKIPIF1<0,SKIPIF1<0,SKIPIF1<0)SKIPIF1<0SKIPIF1<0解：SKIPIF1<0u=2x-1,SKIPIF1<0=2du=2dx∴SKIPIF1<0SKIPIF1<0SKIPIF1<0解：SKIPIF1<0u=x,SKIPIF1<0,SKIPIF1<0SKIPIF1<0四、應(yīng)用題（本題16分）用鋼板焊接一個容積為4SKIPIF1<0的底為正方形的無蓋水箱，已知鋼板每平方米10元，焊接費40元，問水箱的尺寸如何選擇，可使總費最低？最低總費是多少？解：設(shè)水箱的底邊長為x，高為h,表面積為s，且有h=SKIPIF1<0所以S(x)=x2+4xh=x2+SKIPIF1<0SKIPIF1<0令SKIPIF1<0（x）=0，得x=2因為本問題存在最小值，且函數(shù)的駐點唯一，所以x=2，h=1時水箱的表面積最小。此時的費用為S（2）×10+40=160元欲用圍墻圍成面積為216平方米的一塊矩形的土地，并在正中用一堵墻將其隔成兩塊，問這塊土地的長和寬各選取多大尺寸，才能使所用建筑材料最??？設(shè)長方形一邊長為x，∵S=216∴另一邊長為216/x∴總材料y=2x+3·216/x=2x+SKIPIF1<0y′=2+648·(x-1)′=2+648·(-1·)=2-SKIPIF1<0y′=0得2=SKIPIF1<0∴x2=324∴x=18∴一邊長為18，一邊長為12時，用料最省.欲做一個底為正方形，容積為32立方米的長方體開口容器，怎樣做法用料最?。吭O(shè)底邊長為a∴底面積為a2a2h=v=32∴h=SKIPIF1<0∴表面積為a2+4ah=a2+4a·SKIPIF1<0=a2+SKIPIF1<0y=a2+SKIPIF1<0,y′=2a+128·(-SKIPIF1<0)=2a-SKIPIF1<0y′=0得2a=SKIPIF1<0∴a3=64∴a=4∴底面邊長為4，h=SKIPIF1<0=2設(shè)矩形的周長為120厘米，以矩形的一邊為軸旋轉(zhuǎn)一周得一圓柱體。試求矩形的邊長為多少時，才能使圓柱體的體積最大。解：設(shè)矩形一邊長為x，另一邊為60-x以AD為軸轉(zhuǎn)一周得圓柱，底面半徑x，高60-x∴V=SKIPIF1<0SKIPIF1<0SKIPIF1<0得：SKIPIF1<0∴矩形一邊長為40，另一邊長為20時，Vmax

作業(yè)（一）————函數(shù)，極限和連續(xù)一、填空題（每小題2分，共20分）1.函數(shù)SKIPIF1<0的定義域是．答案：SKIPIF1<02．函數(shù)SKIPIF1<0的定義域是．答案：SKIPIF1<03.函數(shù)SKIPIF1<0的定義域是．答案：SKIPIF1<04.函數(shù)SKIPIF1<0，則SKIPIF1<0 ．答案：SKIPIF1<05．函數(shù)SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<06．函數(shù)SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<07．函數(shù)SKIPIF1<0的間斷點是．答案：SKIPIF1<08.SKIPIF1<0．答案：19．若SKIPIF1<0，則SKIPIF1<0．答案：210．若SKIPIF1<0，則SKIPIF1<0．答案：1.5；二、單項選擇題（每小題2分，共24分）1．設(shè)函數(shù)SKIPIF1<0，則該函數(shù)是（）．答案：BA．奇函數(shù)B．偶函數(shù)C．非奇非偶函數(shù)D．既奇又偶函數(shù)2．設(shè)函數(shù)SKIPIF1<0，則該函數(shù)是（）．答案：AA．奇函數(shù)B．偶函數(shù)C．非奇非偶函數(shù)D．既奇又偶函數(shù)3．函數(shù)SKIPIF1<0的圖形是關(guān)于（）對稱．答案：DA．SKIPIF1<0B．SKIPIF1<0軸C．SKIPIF1<0軸D．坐標原點4．下列函數(shù)中為奇函數(shù)是（ C）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<05．函數(shù)SKIPIF1<0的定義域為（ ）．答案：DA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0且SKIPIF1<0D．SKIPIF1<0且SKIPIF1<06．函數(shù)SKIPIF1<0的定義域是（）．答案：DA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<07．設(shè)SKIPIF1<0，則SKIPIF1<0（）答案：CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<08．下列各函數(shù)對中，（ ）中的兩個函數(shù)相等．答案：DA．SKIPIF1<0，SKIPIF1<0B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0D．SKIPIF1<0SKIPIF1<09．當SKIPIF1<0時，下列變量中為無窮小量的是（）答案：C.A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<010．當SKIPIF1<0（）時，函數(shù)SKIPIF1<0，在SKIPIF1<0處連續(xù).答案：BA．0B．1C．SKIPIF1<0D．SKIPIF1<011．當SKIPIF1<0（）時，函數(shù)SKIPIF1<0在SKIPIF1<0處連續(xù)答案：DA．0B．1C．SKIPIF1<0D．SKIPIF1<012．函數(shù)SKIPIF1<0的間斷點是（）答案：AA．SKIPIF1<0B．SKIPIF1<0 C．SKIPIF1<0D．無間斷點三、解答題（每小題7分，共56分）⒈計算極限SKIPIF1<0．解SKIPIF1<02．計算極限SKIPIF1<0解SKIPIF1<03.SKIPIF1<0解：原式＝SKIPIF1<04．計算極限SKIPIF1<0解SKIPIF1<05．計算極限SKIPIF1<0．解SKIPIF1<06.計算極限SKIPIF1<0．解SKIPIF1<0SKIPIF1<07．計算極限SKIPIF1<0解SKIPIF1<08．計算極限SKIPIF1<0．解SKIPIF1<0一、填空題（每小題2分，共20分）1．曲線SKIPIF1<0在SKIPIF1<0點的斜率是．答案：SKIPIF1<02．曲線SKIPIF1<0在SKIPIF1<0點的切線方程是．答案：SKIPIF1<03．曲線SKIPIF1<0在點SKIPIF1<0處的切線方程是 ．答案：SKIPIF1<04．SKIPIF1<0．答案：SKIPIF1<0或SKIPIF1<05．若y=x(x–1)(x–2)(x–3)，則SKIPIF1<0(0)= ．答案：SKIPIF1<06．已知SKIPIF1<0，則SKIPIF1<0=．答案：SKIPIF1<07．已知SKIPIF1<0，則SKIPIF1<0=．答案：SKIPIF1<08．若SKIPIF1<0，則SKIPIF1<0 ．答案：SKIPIF1<09．函數(shù)SKIPIF1<0的單調(diào)增加區(qū)間是．答案：SKIPIF1<010．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)單調(diào)增加，則a應(yīng)滿足 ．答案：SKIPIF1<0二、單項選擇題（每小題2分，共24分）1．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0是（）答案：DA．單調(diào)增加B．單調(diào)減少C．先增后減D．先減后增2．滿足方程SKIPIF1<0的點一定是函數(shù)SKIPIF1<0的（）答案：C.A．極值點B．最值點C．駐點D．間斷點3．若SKIPIF1<0，則SKIPIF1<0=（）．答案：CA.2B.1C.-1D.–24．設(shè)SKIPIF1<0，則SKIPIF1<0（）．答案：BA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<05．設(shè)SKIPIF1<0是可微函數(shù)，則SKIPIF1<0（）．答案：DA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<06．曲線SKIPIF1<0在SKIPIF1<0處切線的斜率是（）．答案：CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<07．若SKIPIF1<0，則SKIPIF1<0（）．答案：CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<08．若SKIPIF1<0，其中SKIPIF1<0是常數(shù)，則SKIPIF1<0（）．答案CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<09．下列結(jié)論中（A）不正確．答案：CA．SKIPIF1<0在SKIPIF1<0處連續(xù)，則一定在SKIPIF1<0處可微.B．SKIPIF1<0在SKIPIF1<0處不連續(xù)，則一定在SKIPIF1<0處不可導(dǎo).C．可導(dǎo)函數(shù)的極值點一定發(fā)生在其駐點上.D．若SKIPIF1<0在[a，b]內(nèi)恒有SKIPIF1<0，則在[a，b]內(nèi)函數(shù)是單調(diào)下降的.10．若函數(shù)f(x)在點x0處可導(dǎo)，則()是錯誤的．答案：BA．函數(shù)f(x)在點x0處有定義B．SKIPIF1<0，但SKIPIF1<0C．函數(shù)f(x)在點x0處連續(xù)D．函數(shù)f(x)在點x0處可微11．下列函數(shù)在指定區(qū)間SKIPIF1<0上單調(diào)增加的是（）．答案：BA．sinxB．exC．x2 D．3–x12.下列結(jié)論正確的有（ ）．答案：AA．x0是f(x)的極值點，且SKIPIF1<0(x0)存在，則必有SKIPIF1<0(x0)=0B．x0是f(x)的極值點，則x0必是f(x)的駐點C．若SKIPIF1<0(x0)=0，則x0必是f(x)的極值點D．使SKIPIF1<0不存在的點x0，一定是f(x)的極值點三、解答題（每小題7分，共56分）1設(shè)SKIPIF1<0，求SKIPIF1<0．解SKIPIF1<0SKIPIF1<0或SKIPIF1<02．設(shè)SKIPIF1<0，求SKIPIF1<0.解SKIPIF1<03．設(shè)SKIPIF1<0，求SKIPIF1<0.解SKIPIF1<04．設(shè)SKIPIF1<0，求SKIPIF1<0.解SKIPIF1<0或SKIPIF1<05．設(shè)SKIPIF1<0是由方程SKIPIF1<0確定的隱函數(shù)，求SKIPIF1<0.解對方程兩邊同時對x求微分，得SKIPIF1<06．設(shè)SKIPIF1<0是由方程SKIPIF1<0確定的隱函數(shù)，求SKIPIF1<0.解原方程可化為SKIPIF1<0，SKIPIF1<0SKIPIF1<07．設(shè)SKIPIF1<0是由方程SKIPIF1<0確定的隱函數(shù)，求SKIPIF1<0.解：方程兩邊同時對SKIPIF1<0求微分，得SKIPIF1<0SKIPIF1<0SKIPIF1<0.8．設(shè)SKIPIF1<0，求SKIPIF1<0．解：方程兩邊同時對SKIPIF1<0求微分，得SKIPIF1<0SKIPIF1<0一、填空題（每小題2分，共20分）1．若SKIPIF1<0的一個原函數(shù)為SKIPIF1<0，則SKIPIF1<0。答案：`SKIPIF1<0（c為任意常數(shù)）或SKIPIF1<02．若SKIPIF1<0的一個原函數(shù)為SKIPIF1<0，則SKIPIF1<0。答案：SKIPIF1<0或SKIPIF1<03．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<0或SKIPIF1<04．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<0或SKIPIF1<05．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<06．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<07．SKIPIF1<0 SKIPIF1<0 ．答案：SKIPIF1<08．SKIPIF1<0 ．答案：SKIPIF1<09．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<010．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<0二、單項選擇題（每小題2分，共16分）1．下列等式成立的是（）．答案：AA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<03．若SKIPIF1<0，則SKIPIF1<0（）.答案：AA.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<04．若SKIPIF1<0，則SKIPIF1<0（）.答案：AA.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<05．以下計算正確的是（）答案：AA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0SKIPIF1<06．SKIPIF1<0（）答案：AA.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<07．SKIPIF1<0=（ ）．答案：CA．SKIPIF1<0B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．如果等式SKIPIF1<0，則SKIPIF1<0（）答案BA.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<0三、計算題（每小題7分，共35分）1．SKIPIF1<0解SKIPIF1<0或SKIPIF1<02．SKIPIF1<0解SKIPIF1<03．SKIPIF1<0解SKIPIF1<04．SKIPIF1<0SKIPIF1<05．SKIPIF1<0解SKIPIF1<0四、極值應(yīng)用題（每小題12分，共24分）1．設(shè)矩形的周長為120厘米，以矩形的一邊為軸旋轉(zhuǎn)一周得一圓柱體。試求矩形的邊長為多少時，才能使圓柱體的體積最大。1．解：設(shè)矩形SKIPIF1<0的一邊SKIPIF1<0厘米，則SKIPIF1<0厘米，當它沿直線SKIPIF1<0旋轉(zhuǎn)一周后，得到圓柱的體積SKIPIF1<0令SKIPIF1<0得SKIPIF1<0當SKIPIF1<0時，SKIPIF1<0；當SKIPIF1<0時，SKIPIF1<0.SKIPIF1<0是函數(shù)SKIPIF1<0的極大值點，也是最大值點.此時SKIPIF1<0答：當矩形的邊長分別為20厘米和40厘米時，才能使圓柱體的體積最大.SKIPIF1<02．欲用圍墻圍成面積為216平方米的一成矩形的土地，并在正中用一堵墻將其隔成兩塊，問這塊土地的長和寬選取多大尺寸，才能使所用建筑材料最??？2.解：設(shè)成矩形有土地的寬為SKIPIF1<0米，則長為SKIPIF1<0米，于是圍墻的長度為SKIPIF1<0令SKIPIF1<0得SKIPIF1<0 SKIPIF1<0易知，當SKIPIF1<0時，SKIPIF1<0取得唯一的極小值即最小值，此時SKIPIF1<0答：這塊土地的長和寬分別為18米和12米時，才能使所用的建筑材料最省.五、證明題（本題5分）1函數(shù)SKIPIF1<0在（SKIPIF1<0是單調(diào)增加的．SKIPIF1<0一、填空題（每小題2分，共20分）1．SKIPIF1<0答案：SKIPIF1<02．SKIPIF1<0答案：SKIPIF1<0或23．已知曲線SKIPIF1<0在任意點SKIPIF1<0處切線的斜率為SKIPIF1<0，且曲線過SKIPIF1<0，則該曲線的方程是。答案：SKIPIF1<0或SKIPIF1<04．若SKIPIF1<0．答案：2或45．由定積分的幾何意義知，SKIPIF1<0=。答案：SKIPIF1<06．SKIPIF1<0.答案：07．SKIPIF1<0=．答案：SKIPIF1<08．微分方程SKIPIF1<0的特解為.答案：1或SKIPIF1<09．微分方程SKIPIF1<0的通解為.答案：SKIPIF1<0或SKIPIF1<010．微分方程SKIPIF1<0的階數(shù)為．答案：2或4二、單項選擇題（每小題2分，共20分）1．在切線斜率為2x的積分曲線族中，通過點（1,4）的曲線為（）．答案：AA．y=x2+3B．y=x2+4C．SKIPIF1<0D．SKIPIF1<02．若SKIPIF1<0=2，則k=（）．答案：AA．1B．-1C．0D．SKIPIF1<03．下列定積分中積分值為0的是（）．答案：AA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<04．設(shè)SKIPIF1<0是連續(xù)的奇函數(shù)，則定積分SKIPIF1<0（）答案：D5．SKIPIF1<0（）．答案：DA．0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<06．下列無窮積分收斂的是（）．答案：BA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<07．下列無窮積分收斂的是（）．答案：BA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<08．下列微分方程中，（ ）是線性微分方程．答案：DA．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．微分方程SKIPIF1<0的通解為（）．答案：CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<010．下列微分方程中為可分離變量方程的是（）答案：BA.SKIPIF1<0；B.SKIPIF1<0；C.SKIPIF1<0；D.SKIPIF1<0三、計算題（每小題7分，共56分）1．SKIPIF1<0解SKIPIF1<0SKIPIF1<0或SKIPIF1<02．SKIPIF1<0解SKIPIF1<03．SKIPIF1<0解利用分部積分法SKIPIF1<0SKIPIF1<04．SKIPIF1<0SKIPIF1<05．SKIPIF1<0SKIPIF1<06．求微分方程SKIPIF1<0滿足初始條件SKIPIF1<0的特解．SKIPIF1<0SKIPIF1<0即通解SKIPIF1<07．求微分方程SKIPIF1<0的通解。SKIPIF1<0SKIPIF1<0即通解為SKIPIF1<0.四、證明題（本題4分）證明等式SKIPIF1<0。SKIPIF1<0

作業(yè)（一）————函數(shù)，極限和連續(xù)一、填空題（每小題2分，共20分）1.函數(shù)SKIPIF1<0的定義域是．答案：SKIPIF1<02．函數(shù)SKIPIF1<0的定義域是．答案：SKIPIF1<03.函數(shù)SKIPIF1<0的定義域是．答案：SKIPIF1<04.函數(shù)SKIPIF1<0，則SKIPIF1<0 ．答案：SKIPIF1<05．函數(shù)SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<06．函數(shù)SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<07．函數(shù)SKIPIF1<0的間斷點是．答案：SKIPIF1<08.SKIPIF1<0．答案：19．若SKIPIF1<0，則SKIPIF1<0．答案：210．若SKIPIF1<0，則SKIPIF1<0．答案：1.5；二、單項選擇題（每小題2分，共24分）1．設(shè)函數(shù)SKIPIF1<0，則該函數(shù)是（）．答案：BA．奇函數(shù)B．偶函數(shù)C．非奇非偶函數(shù)D．既奇又偶函數(shù)2．設(shè)函數(shù)SKIPIF1<0，則該函數(shù)是（）．答案：AA．奇函數(shù)B．偶函數(shù)C．非奇非偶函數(shù)D．既奇又偶函數(shù)3．函數(shù)SKIPIF1<0的圖形是關(guān)于（）對稱．答案：DA．SKIPIF1<0B．SKIPIF1<0軸C．SKIPIF1<0軸D．坐標原點4．下列函數(shù)中為奇函數(shù)是（ C）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<05．函數(shù)SKIPIF1<0的定義域為（ ）．答案：DA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0且SKIPIF1<0D．SKIPIF1<0且SKIPIF1<06．函數(shù)SKIPIF1<0的定義域是（）．答案：DA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<07．設(shè)SKIPIF1<0，則SKIPIF1<0（）答案：CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<08．下列各函數(shù)對中，（ ）中的兩個函數(shù)相等．答案：DA．SKIPIF1<0，SKIPIF1<0B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0D．SKIPIF1<0SKIPIF1<09．當SKIPIF1<0時，下列變量中為無窮小量的是（）答案：C.A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<010．當SKIPIF1<0（）時，函數(shù)SKIPIF1<0，在SKIPIF1<0處連續(xù).答案：BA．0B．1C．SKIPIF1<0D．SKIPIF1<011．當SKIPIF1<0（）時，函數(shù)SKIPIF1<0在SKIPIF1<0處連續(xù)答案：DA．0B．1C．SKIPIF1<0D．SKIPIF1<012．函數(shù)SKIPIF1<0的間斷點是（）答案：AA．SKIPIF1<0B．SKIPIF1<0 C．SKIPIF1<0D．無間斷點三、解答題（每小題7分，共56分）⒈計算極限SKIPIF1<0．解SKIPIF1<02．計算極限SKIPIF1<0解SKIPIF1<03.SKIPIF1<0解：原式＝SKIPIF1<04．計算極限SKIPIF1<0解SKIPIF1<05．計算極限SKIPIF1<0．解SKIPIF1<06.計算極限SKIPIF1<0．解SKIPIF1<0SKIPIF1<07．計算極限SKIPIF1<0解SKIPIF1<08．計算極限SKIPIF1<0．解SKIPIF1<0一、填空題（每小題2分，共20分）1．曲線SKIPIF1<0在SKIPIF1<0點的斜率是．答案：SKIPIF1<02．曲線SKIPIF1<0在SKIPIF1<0點的切線方程是．答案：SKIPIF1<03．曲線SKIPIF1<0在點SKIPIF1<0處的切線方程是 ．答案：SKIPIF1<04．SKIPIF1<0．答案：SKIPIF1<0或SKIPIF1<05．若y=x(x–1)(x–2)(x–3)，則SKIPIF1<0(0)= ．答案：SKIPIF1<06．已知SKIPIF1<0，則SKIPIF1<0=．答案：SKIPIF1<07．已知SKIPIF1<0，則SKIPIF1<0=．答案：SKIPIF1<08．若SKIPIF1<0，則SKIPIF1<0 ．答案：SKIPIF1<09．函數(shù)SKIPIF1<0的單調(diào)增加區(qū)間是．答案：SKIPIF1<010．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)單調(diào)增加，則a應(yīng)滿足 ．答案：SKIPIF1<0二、單項選擇題（每小題2分，共24分）1．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0是（）答案：DA．單調(diào)增加B．單調(diào)減少C．先增后減D．先減后增2．滿足方程SKIPIF1<0的點一定是函數(shù)SKIPIF1<0的（）答案：C.A．極值點B．最值點C．駐點D．間斷點3．若SKIPIF1<0，則SKIPIF1<0=（）．答案：CA.2B.1C.-1D.–24．設(shè)SKIPIF1<0，則SKIPIF1<0（）．答案：BA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<05．設(shè)SKIPIF1<0是可微函數(shù)，則SKIPIF1<0（）．答案：DA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<06．曲線SKIPIF1<0在SKIPIF1<0處切線的斜率是（）．答案：CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<07．若SKIPIF1<0，則SKIPIF1<0（）．答案：CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<08．若SKIPIF1<0，其中SKIPIF1<0是常數(shù)，則SKIPIF1<0（）．答案CA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<09．下列結(jié)論中（A）不正確．答案：CA．SKIPIF1<0在SKIPIF1<0處連續(xù)，則一定在SKIPIF1<0處可微.B．SKIPIF1<0在SKIPIF1<0處不連續(xù)，則一定在SKIPIF1<0處不可導(dǎo).C．可導(dǎo)函數(shù)的極值點一定發(fā)生在其駐點上.D．若SKIPIF1<0在[a，b]內(nèi)恒有SKIPIF1<0，則在[a，b]內(nèi)函數(shù)是單調(diào)下降的.10．若函數(shù)f(x)在點x0處可導(dǎo)，則()是錯誤的．答案：BA．函數(shù)f(x)在點x0處有定義B．SKIPIF1<0，但SKIPIF1<0C．函數(shù)f(x)在點x0處連續(xù)D．函數(shù)f(x)在點x0處可微11．下列函數(shù)在指定區(qū)間SKIPIF1<0上單調(diào)增加的是（）．答案：BA．sinxB．exC．x2 D．3–x12.下列結(jié)論正確的有（ ）．答案：AA．x0是f(x)的極值點，且SKIPIF1<0(x0)存在，則必有SKIPIF1<0(x0)=0B．x0是f(x)的極值點，則x0必是f(x)的駐點C．若SKIPIF1<0(x0)=0，則x0必是f(x)的極值點D．使SKIPIF1<0不存在的點x0，一定是f(x)的極值點三、解答題（每小題7分，共56分）1設(shè)SKIPIF1<0，求SKIPIF1<0．解SKIPIF1<0SKIPIF1<0或SKIPIF1<02．設(shè)SKIPIF1<0，求SKIPIF1<0.解SKIPIF1<03．設(shè)SKIPIF1<0，求SKIPIF1<0.解SKIPIF1<04．設(shè)SKIPIF1<0，求SKIPIF1<0.解SKIPIF1<0或SKIPIF1<05．設(shè)SKIPIF1<0是由方程SKIPIF1<0確定的隱函數(shù)，求SKIPIF1<0.解對方程兩邊同時對x求微分，得SKIPIF1<06．設(shè)SKIPIF1<0是由方程SKIPIF1<0確定的隱函數(shù)，求SKIPIF1<0.解原方程可化為SKIPIF1<0，SKIPIF1<0SKIPIF1<07．設(shè)SKIPIF1<0是由方程SKIPIF1<0確定的隱函數(shù)，求SKIPIF1<0.解：方程兩邊同時對SKIPIF1<0求微分，得SKIPIF1<0SKIPIF1<0SKIPIF1<0.8．設(shè)SKIPIF1<0，求SKIPIF1<0．解：方程兩邊同時對SKIPIF1<0求微分，得SKIPIF1<0SKIPIF1<0一、填空題（每小題2分，共20分）1．若SKIPIF1<0的一個原函數(shù)為SKIPIF1<0，則SKIPIF1<0。答案：`SKIPIF1<0（c為任意常數(shù)）或SKIPIF1<02．若SKIPIF1<0的一個原函數(shù)為SKIPIF1<0，則SKIPIF1<0。答案：SKIPIF1<0或SKIPIF1<03．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<0或SKIPIF1<04．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<0或SKIPIF1<05．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<06．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<07．SKIPIF1<0 SKIPIF1<0 ．答案：SKIPIF1<08．SKIPIF1<0 ．答案：SKIPIF1<09．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<010．若SKIPIF1<0，則SKIPIF1<0．答案：SKIPIF1<0二、單項選擇題（每小題2分，共16分）1．下列等式成立的是（）．答案：AA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<03．若SKIPIF1<0，則SKIPIF1<0（）.答案：AA.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<04．若SKIPIF1<0，則SKIPIF1<0（）.答案：AA.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<05．以下計算正確的是（）答案：AA．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0SKIPIF1<06．SKIPIF1<0（）答案：AA.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<07．SKIPIF1<0=（ ）．答案：CA．SKIPIF1<0B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．如果等式SKIPIF1<0，則SKIPIF1<0（）答案BA.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<0三、計算題（每小題7分，共35分）1．SKIPIF1<0解SKIPIF1<