2017年江苏省专转本高数不定积分模拟试题练习(含答案)

江苏省专转本（高等数学）模拟试卷37(题后含答案及解析)题型有：1. 选择题 2. 填空题 4. 解答题 5. 综合题 6. 证明题选择题在每小题给出的四个选项中，只有一项是符合要求的。

1．若x→0时，(1-ax2)1／4-1与xsinx是等价无穷小，则a=( )．A．1B．-4C．4D．3正确答案：B解析：当x→0时，(1-ax2)1／4-1～-ax2，xsinxax～x2于是，根据题设有故a=-4．2．下列函数中，在[-1，1]上满足罗尔中值定理条件的是( )．A．f(x)=B．f(x)=x+5C．f(x)=D．f(x)=x+1正确答案：A解析：B、C和D不满足罗尔定理的f(a)=f(b)条件．3．设I=∫01dy∫02yf(x，y)dx+∫13dy∫03-yf(x，y)dx，交换积分次序后I=( )．A．∫03dx∫03-xf(x，y)dyB．∫02dx∫03-xf(x，y)dyC．∫02dx f(x，y)dyD．∫03dxf(x，y)dy正确答案：C4．已知y=ln(x+)，则下列正确的是( )．A．B．C．D．正确答案：C解析：y=ln(x+5．xyy’=1，y(1)=1的解是( )．A．xB．y2=2lnx+1C．y2=lnxD．y2=x正确答案：B解析：xyy’=1y2=2lnx+C.又因为f(1)=1所以1=2ln1+C，那么C=1，所以y2=2lnx+1．6．设un为正项级数，如下说法正确的是( )．A．B．C．D．正确答案：C解析：选项A当un取1／n时，不对，排除．B选项0≤t＜∞不对，应是l＜1，un必收敛，D仍然可用∑是发散的，故排除，所以选C.填空题7．(1+2x)3／x=_______．正确答案：e6解析：=e68．设f(x)=在x=0处连续，则a=_______．正确答案：-1解析：a=-1．9．y=2ln+1的水平渐近线是_______．正确答案：y=1解析：10．∫-∞+∞dx=1，则是的值为_______．正确答案：1／π解析：k．∫-∞+∞11．设曲线y=x2+x+2上点M处的斜率为-3，则点M的坐标是_______．正确答案：(-2，4)解析：y’=2x+1=-3x=-2，代入到原方程得y=4．12．设向量a，b，令|a+b|=|a-b|，a={3，-5，8)，b={-1，1，z}．则z=_______．正确答案：1解析：因为a+b={2，-4，8+z}，a-b={4，-6，8-z)，由|a+b|=|a-b|有，解得z=1．解答题解答时应写出推理、演算步骤。

专转本数学导数与微分模拟试题练习一、选择题1．设函数在处连续，则（）A．必存在B．必存在C．不存在D．不一定等于2．如果在处可导，则（）A．B．C．D．0 3．设在的邻域内连续，且有，则（）A．B．C．D．04．设为可导的偶函数，则为( )A．偶函数B．可能是偶函数C．奇函数D．非奇非偶函数5．下列函数中（）在处可导A．B．C．D．6．设函数在处可导，则有（）A．B．C．D．7．设，则在处（）A．可导且B．不可导C．取得极小值D．取得极大值8．设，则（）A．B．C．D．9．曲线在（1，0）点的切线为（）A．不存在B．C．D．10．设函数由参数方程所确定，则（）A．B．1 C．D．11．设，则（）A．B．C．D．二、填空题1．设，则．2．设存在，且，则．3．设，则．4．设，则．5．设函数在处可导，且，，则．6．设，则．7．设方程确定是的函数，则．8．曲线在点（0，1）的法线方程为．9．设，其中函数可微，且，．10．设=，为使在点连续，须补充定义，此时．三、求下列函数的导数或微分（1），求；（2），求；（3）设，求（4），其中，求四、（1）若函数由方程确定，求（2）设，二阶可导，且，求一、1．B；2．C；3．B；4．C；5．B；6．C；7．C；8．A；9．A；10．C二、1．；2．0；3．；4．；5．2；6．；7．；8．法线方程为；9．=7；10．，1．三、（1）；（2）[]．（3）=．（4）．四、（1）；（2）．。

江苏省专转本（高等数学）模拟试卷44(题后含答案及解析) 题型有：1. 选择题 2. 填空题 4. 解答题 5. 综合题 6. 证明题选择题在每小题给出的四个选项中，只有一项是符合要求的。

1．已知连续函数f(x)满足f(x)=x2+x∫01f(x)dx，则f(x)=( )．A．f(x)=x2+xB．f(x)=x2一xC．D．正确答案：C解析：用代入法可得出正确答案为C2．函数在x=0处( )．A．连续但不可导B．连续且可导C．不连续也不可导D．可导但不连续正确答案：B解析：3．关于的间断点说法正确的是( )．A．为可去间断点B．x=0为可去间断点C．x=kπ为第二类无穷间断点D．以上说法都正确正确答案：D解析：的间断点为为可去间断点．对于x=kx，当k=0，即x=0时，x=0为可去间断点．当k≠0时，为第二类无穷间断点．4．设D：x2+y2≤R2，则=( )．A．B．∫0 2πdθ∫0Rrdr=πR2C．D．∫02πdθ∫0RR2dr=2πR正确答案：C解析：在极坐标中，0≤r≤，R，0≤θ≤2π，5．抛物面在点M0(1，2，3)处的切平面是( )．A．6x+3y一2z一18=0B．6x+3y+2z一18=0C．6x+3y+2z+18=0D．6x一3y+2z一18=0正确答案：B解析：6．幂级数的收敛半径是( )．A．0B．1C．2D．+∞正确答案：B解析：填空题7．则a=________，b=________．正确答案：一4；3解析：并且x2+ax+b=0，所以a=一4，b=3．8．u=f(xy，x2+2y2)，其中f为可微函数，则=________。

正确答案：yf1+2xf’2解析：令w=xy，v=x2+y2，则u=f(w，v)，9．已知函数f(x)=alnx+bx2+x在x=1与x=2处有极值，则a=____________，b=_______________．正确答案：解析：由题意可知：10．a，b为两个非零矢量，λ为非零常数，若向量a+λb垂直于向量b，则λ等于___________．正确答案：解析：a+λb垂直于向量b→(a+λb).b=0．11．已知f(cosx)=sin2x，则∫f(x一1)dx=___________．正确答案：解析：12．已知f(x)=ex2，f[φ(x)]=1一x，且φ(x)≥0，则φ(x)的定义域为_____________．正确答案：x≤0解析：解答题解答时应写出推理、演算步骤。

[专升本类试卷]江苏省专转本（高等数学）模拟试卷28一、选择题在每小题给出的四个选项中，只有一项是符合要求的。

1 已知f(0)=0，f'(0)=1，（A）1（B）0（C）一1（D）不存在2 若∫f(x)dx=，则f'(x)等于( )．3 当x＞0时，（A）高阶无穷小量（B）低阶无穷小量（C）同阶，但不等价无穷小量（D）等价无穷小量4 方程x2+y2=4x在空间直角坐标系中表示( )．（A）圆柱面（B）点（C）圆（D）旋转抛物面5 若广义积分收敛，则p应满足( )．（A）0＜p＜1（B）p＞1（C）p＜一1（D）p＜06 设对一切x有f(一x，y)=一f(x，y)，D={(x，y)|x2+y2≤1，y≥0)，D1={(x，y)|x2+y2≤1，x≥0，y≥0}，则二、填空题78 设f(x)为连续奇函数，则f(0)=______．910 已知．|a|=4，|b|=5，则|a+b|=______．11 若直线y=5x+m是曲线y=x2+3x+2的一条切线，则常数m=________．12三、解答题解答时应写出推理、演算步骤。

13 求的极限．14 求∫(2x一1)ln2xdx．15 计算定积分16 已知17 解常微分方程：18 将函数f(x)=展开为x的幂级数，并指出收敛区间．19 求过点(1，2，3)且垂直于直线的平面方程．20 如图所示，D为x2+y2≤a2与x≥0所围的区域，计算四、综合题21 求出满足下列条件的最低次多项式：当x=1时有极大值6，当x=3时有极小值2．22 设曲线过曲线(2，2)点处的切线与曲线及y轴所围成平面图形的面积，并求出平面图形绕x轴旋转的旋转体的体积.五、证明题23 证明：。

江苏省专转本（高等数学）模拟试卷2(题后含答案及解析)题型有：1. 选择题 2. 填空题 4. 解答题 5. 综合题 6. 证明题选择题在每小题给出的四个选项中，只有一项是符合要求的。

1．已知连续函数f(x)满足f(x)=x2+x∫01f(x)dx，则f(x)=( )。

A．f(x)=x2+xB．f(x)=x2-xC．f(x)=x2+D．f(x)=x2+正确答案：C解析：用代入法可得出正确答案为C。

2．函数在x=0处( )。

A．连续但不可导B．连续且可导C．不连续也不可导D．可导但不连续正确答案：B解析：3．关于的间断点说法正确的是( )。

A．x=kπ+为可去间断点B．x=0为可去间断点C．x=kπ为第二类无穷间断点D．以上说法都正确正确答案：D解析：对于x=kπ，当k=0，即x=0时，，x=0为可去间断点。

当k≠0时，，x=kπ为第二类无穷间断点。

4．设D：x2+y2≤R2，则=( )。

A．＝πR3B．∫02πdθ∫0Rrdr＝πR2C．∫02πdθ∫0Rr2dr＝πR3D．∫02πdθ∫0RR2dr＝2πR3正确答案：C解析：在极坐标中，0≤r≤R，0≤θ≤2π，。

5．抛物面在点M0(1，2，3)处的切平面是( )。

A．6x+3y-2z-18=0B．6x+3y+2z-18=0C．6x+3y+2z+18=0D．6x-3y+2z-18=0正确答案：B解析：设切平面方程为6x+3y+2z-18=0。

6．幂级数的收敛半径是( )。

A．0B．1C．2D．+∞正确答案：B解析：，收敛半径。

填空题7．，则a=＿＿＿＿＿＿，b=＿＿＿＿＿＿。

正确答案：-4，3解析：并且x2+ax+b=0，所以a=-4，b=3。

8．u=f(xy，x2+2y2)，其中f为可微函数，则＝＿＿＿＿＿＿。

正确答案：yf’1+2xf’2解析：令w=xy，v=x2+y2，则u=f(w，v)，=f’w(w，v)·y+f’v(w，v)·2x。

江苏省专转本（高等数学）模拟试卷43(题后含答案及解析) 题型有：1. 选择题 2. 填空题 4. 解答题 5. 综合题 6. 证明题选择题在每小题给出的四个选项中，只有一项是符合要求的。

1．已知f(x)=2|x|，则f’(0)=( )．A．2|x|ln2B．2xln2C．2-xln2D．不存在正确答案：D2．下列积分收敛的是( )．A．B．C．D．正确答案：B3．下列极限中正确的是( )．A．B．C．D．正确答案：C4．y=xx，则下列正确的是( )．A．y’=xx-1B．dy=xxlnxdxC．y’=xx(lnx+1)D．y’=xxdx正确答案：C5．与平面x+y+z=1平行的直线方程是( )．A．B．x一1=y一1=z一2C．D．x一2y+z=3正确答案：C6．下列哪个结论是正确的( ).A．收敛B．绝对收敛C．绝对收敛D．收敛正确答案：C填空题7．=___________.正确答案：eε解析：8．设在x=0处连续，则a=_____________．正确答案：一1解析：9．的水平渐近线是_________．正确答案：y=1解析：10．,则k的值为________．正确答案：解析：11．设曲线y=x2+x+2上点M处的斜率为一3，则点M的坐标是_________．正确答案：(一2，4)解析：y’=2x+1=一3→=x=一2，代入到原方程得y=4．12．设向量a，b，令｜a+b｜=｜a一b｜，a=(3，一5，8)，b={一1，1，z}．则z=__________．正确答案：1解析：因为a+b={2，一4，8+z)，a一b={4，一6，8一z)，由｜a+b｜=｜a 一b｜有解答题解答时应写出推理、演算步骤。

13．设函数y=y(x)由方程ex-ey=xy确定，求。

正确答案：方程ex一ey=xy，两边对x求导数得ex一ey.y’=y+xy’，故14．y=(1一x2)cosx，求y(n)．正确答案：y(n)=(1一x2)(cosx)2(n)+Cn1(1一x2)’(cosx)(n-1)，Cm2(1一x2)’’(cosx)(n-2)[*]15．求正确答案：设16．计算定积分正确答案：设17．计算正确答案：18．求微分方程x2y’=xy—y2的通解．正确答案：将原方程变形为：则y’=P+xp’，代入原方程得：xp’=一p2，分离变量得，两边积分，得19．z=f(x2一y2，xy)，求正确答案：20．已知(1)f(x)在x=0处连续，求a；(2)求f’(x)．正确答案：综合题21．设函数y=f(x)满足方程xy’+y=x，且．(1)求f(x)；(2)求f(x)的单调增加区间．正确答案：(1)经整理得一阶线性微分方程22．某公司年产量为x百台机床，总成本为C万元，其中固定成本为2万元，每产1百台增加1万元，市场上每年可销售此商品4百台，其销售总收入R(x)(单位：万元)是x的函数，问每年生产多少台利润最大?正确答案：设每年的产量为x百台时利润为y万元．故每年生产3百台时利润最大为万元．23．若f(x)在x=0处连续，求k，a的值．正确答案：根据连续的条件：证明题24．证明：当｜x｜≤1时，则｜4x一x4｜≤5成立．正确答案：令f(x)=4x一x4，则f’(x)=4—4x3=0，x=1．所以f(一1)=一4—1=一5，f(1)=4—1=3．故fmax(x)=3，fmin(x)=一5，所以一5≤f(x)≤3．那么｜4x一x4｜≤5成立．。

江苏省普通高校专转本模拟试题及参考答案高等数学 试题卷一、单项选择题（本大题共 8 小题，每小题 4 分,共 32 分.在下列每小题中选出一个正确答 案，请在答题卡上将所选项的字母标号涂黑）1. 要使函数21()(2)xx f x x −−=−在区间(0,2) 内连续，则应补充定义 f (1) =（ ）A. 2eB. 1e −C. eD. 2e − 2. 函数2sin ()(1)xf x x x =−的第一类间断点的个数为（ ）A. 0B. 2C. 3D. 1 3. 设'()1f x =，则0(22)(22)limh f h f h h→−−+=（ ）A. 2−B. 2C. 4D. 4−4.设()F x 是函数()f x 的一个原函数，且()f x 可导，则下列等式正确的是（ ） A. ()()dF x f x c =+∫ B. ()()df x F x c =+∫ C.()()F x dx f x c =+∫ D.()()f x dx F x c =+∫5. 设2Dxdxdy =∫∫，其中222{(,)|,0}D x y x y R x =+≤>，则R 的值为（ ）A. 1B.D.6.下列级数中发散的是（ ）A 21sin n nn∞=∑. B. 11sin n n ∞=∑C. 1(1)nn ∞=−∑ D.211(1)sinnn n ∞=−∑ 7.若矩阵11312102A a −−= 的秩为2，则常数a 的值为（ ）A. 0B. 1C. 1−D. 28. 设1100001111111234D =−−，其中ij M 是D 中元素ij a 的余子式，则3132M M +=（ ） A. 2− B. 2 C. 0 D. 1 二、填空题（本大题共6小题，每小题4分，满分24分） 9. 1lim sinn n n→∞=____________________________.10.设函数2sin ,0()10,0xx f x x x ≠ =+ =，则'(0)f =______________________________________.11.设函数()cos 2f x x =, 则(2023)(0)f =__________________________________________. 12.若21ax e dx −∞=∫，则常数a =___________________________________.13. 若幂级数1nnn a x +∞=∑的收敛半径为2，则幂级数11(1)nn n x a +∞=−∑的收敛区间为__________________. 14.若向量组1(1,0,2,0)α=，2(1,0,0,2)α=，3(0,1,1,1)α=，4(2,1,,2)k α=线性相关，则k =_____________________________________.三、计算题（本大题共8小题，每小题8分，满分64分） 15. 求极限22sin lim(cos 1)x x t tdtx x →−∫；16.求不定积分22x x e dx ∫；17.求定积分21sin 2x dx π−∫； 18.设函数(,)z z x y =由方程cos y x e xy yz xz =+++所确定的函数，求全微分dz . 19.求微分方程''4'5x y y y xe −−−=的通解； 20.求二重积分Bxydxdy ∫∫，其中D 为由曲线2(0)y x x ≥及直线2x y +=和y 轴所围成的平面闭区域；21.设矩阵A 与B 满足关系是2AB A B =+，其中301110014A= ，求矩阵B .22.求方程组12341234123436536222x x x x x x x x x x x x ++−=−++=− −+−= 的通解； 四、证明题（本大题10分）23.证明：当04x π−<<时，0sin xt e tdt x <∫.五、综合题（本大题共2小题，每小题10分，满分20分）24.求曲线x =及直线2y =与y 轴所围成的平面图形的面积并计算该图形绕y 轴旋转一周所得的旋转体的体积..25.设定义在(,)−∞+∞上的函数()f x 满足方程'()()f x f x x −=，且(0)0f =，求： （1）函数()f x 的解析式；（2）曲线()y f x =的单调区间和极值点.参考答案一、单项选择题1. B2. D3. D4. D5. B6. B7. A8. B9. C 二、填空题9. 1 10. 1 11. 0 12. 1ln 2213. (1,3)− 14. 4三、计算题15. 2232022250022sin sin 2sin()4lim lim 4lim (1cos )63()2x x x x x t tdt t tdt x x x x x x x →→→===−∫∫； 16. 2222222222222222222224x x x x x x x xxe e x e e e x e e e x e dx x x dx x dx x c =−=−+=−++∫∫∫；17.26206111sin (sin )(sin )22212x dx x dx x dx πππππ−=−+−−∫∫∫； 18. 因为sin sin ,,z zz x y zx y yz x x x x y x ∂∂∂−−−−=+++=∂∂∂+ 且0,y yz zz e x z e x z y x y yy y x∂∂∂−−−=++++=∂∂∂+ 所以可得sin y x y z e x zdzdx dy y x y x−−−−−−=+++. 19. 解：因为特征方程为2450r r −−=，特征值为125,1r r ==−，所以齐次微分方程''4'50y y y −−=的通解为5112x x y c e c e −=+； 设''4'5x y y y xe −−−=的一个特解为*()x y x ax b e −=+，可得11*()1236x y x x e −=−+，所以原方程的通解为：511211*()1236x x x y y y c e c e x x e −−=+=+−+.20. 由22y x x y =+= 可得交点坐标(11)，， 可得21116xBxydxdydx xydy ==∫∫∫∫； 21. 因为2AB A B =+，所以可得(2)A E B A −=，从而可得：1(2)B A E A −=−；又因1211(2)221111A E −−−−=−−− ，所以可得1522(2)432223B A E A −−− =−=−− − ； 22.求方程组12341234123436536222x x x x x x x x x x x x ++−=−++=− −+−= 的通解； 解：111361113611136101241513601012010120101212212031240011200112100120101200112−−−−−−→−→−→− −−−−−−− →− − 一个特解为2220 ，齐次线性方程组12341234123430530220x x x x x x x x x x x x ++−=−++= −+−= 的一组基础解系为：11111η= ，所以原方程组的通解为：123412121210x x c x x=+. 四、证明题 23.证明：当04x π−<<时，0sin xt e tdt x <∫.证明：令0()sin xt f x x e tdt =−∫，则有'()1sin x f x e x =−，令：''()sin cos 0x x f x e x e x =−−=，可得4x π=−，当04x π−<<，''()0f x <，所以当04x π−<<时，'()1sin x f x e x =−为递减函数，可得'()1sin '(0)1x f x e x f =−>=，所以当04x π−<<时，0()sin xt f x x e tdt =−∫为递增函数，因此可得：0()sin (0)0xt f x x e tdt f =−>=∫，从而可证得：0sin x t e tdt x <∫； 五、综合题 24.求曲线x =及直线2y =与y 轴所围成的平面图形的面积并计算该图形绕y 轴旋转一周所得的旋转体的体积..解：x x y = ⇒ =，则图形面积为：20Aydx dx = 旋转体的体积：2222200022y V x dy ydy ππππ====∫∫； 25.设定义在(,)−∞+∞上的函数()f x 满足方程'()()f x f x x −=，且(0)0f =，求： （1）函数()f x 的解析式；（2）曲线()y f x =的单调区间和极值点. 解：（1）()()()1dxdxx x x f x e xe dx c e xe dx c x ce −−−−−∫∫=+=+=−++∫∫，又因为(0)0f =，所以可得：1c =−，即：()1x f x x e −=−+−； （2）令'()10x f x e −=−+=，可得0x =； x(,0)−∞ 0 (0,)+∞ '()f x −+因此可知：(,0)−∞为函数()1x f x x e −=−+−的递减区间，(0,)+∞为函数()1x f x x e −=−+−的递增区间，点(0,0)为函数()1x f x x e −=−+−的极小值点.。

第三章 不定积分本章主要知识点：● 不定积分的意义，基本公式● 不定积分的三种基本方法● 杂例一、不定积分的意义、基本公式不定积分基本特点是基本公式较多，灵活善变，复习此章节主要诀窍在于：基本公式熟练，基本题型运算快捷，有一定题量的训练。

1．性质()()()f x dx f x '=⎰()()()d f x dx f x dx =⎰⎰+=C x F x dF )()(()()f x dx f x C '=+⎰()(1)()n n f dx f x C -=+⎰2．基本公式（1）11(1)1nn x dx x c n n +=+≠-+⎰，c x dx x +=⎰||ln 1 （2）c a a dx a x x +=⎰ln ，c e dx e x x +=⎰ （3）⎰+-=c x xdx cos sin ，⎰+=c x xdx sin cos ， c x xdx +=⎰tan sec 2，c x xdx +-=⎰cot csc 2第三章 不定积分（4）c ax dx x a +=-⎰arcsin 122， （5）c x a x a a dx x a +-+=-⎰||ln 21122121111f dx f d x x x x ⎛⎫⎛⎫⎛⎫=- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎰⎰ ⎰⎰=x d x f dx x xf tan )(tan )(tan sec 2tan sec (sec )(sec )sec x xf x dx f x d x =⎰⎰ 等等。

例3.1．22007(21)x x dx +⎰解：原式=2200722200811(21)(21)(21)48032x d x x c ++=++⎰ 例3.2．3sin 13sin 13sin 111cos (3sin 1)33x x x xe dx e d x e c ---=-=+⎰⎰ 例3.3．23sin(57)x x dx -⎰解：原式=331sin(57)3x dx -⎰331sin(57)(57)15x d x =--⎰ 31cos(57)15x C =--+ 例3.4．⎰+dx x x x 1ln 2ln 1 解：原式⎰+=x d x x ln 1ln 2ln ⎰+-+=du u u x u 1211221ln =⎰+-du u )1211(21=11ln 2124u u C -++=C x x +++1ln 2ln 41ln 21 例3.5．44x dx x +⎰解：原式=⎰+2222)(2121dx x C x +=2arctan 412 例3.6．221cos (2tan 1)dx x x +⎰解：原式222sec 1tan 12tan 12tan x dx d x x x ==++⎰⎰tan )x C =+例3.7．解：原式2112sin (1cos 2)sin(2)24u du u u C =-=-+⎰⎰14C + 例3.8．⎰+dx e x e x解：原式x x xe x e x e e e dx e de e C =⋅==+⎰⎰第三章 不定积分例3.9．⎰+++dx x x x 2233 解：利用综合除法知12127222323+-+-=+++x x x x x x 原式C x x x x dx x x x ++-+-=+-+-=⎰2ln 12731)21272(232例 例例=x C =+例3.13．sin sin cos x dx x x +⎰解：原式=1(sin cos sin cos )2sin cos x x x x dx x x ++-⋅+⎰=11(cos sin )22sin cos d x x dx x x--++⎰⎰ =11ln sin cos 22x x x c +++ 例3.14．cos 2sin 3cos x dx x x+⎰ 解：令()2sin 3cos f x x x =+，则()2cos 3sin ,f x x x '=-32cos ()()1313x f x f x '=+ 原式＝32()()321313ln |2sin 3cos |()1313f x f x dx x x x C f x '+=+++⎰ 例3.15．2212sin cos dx x x +⎰解：原式＝222sec 1tan )2tan 12tan 1x dx d x x C x x ==+++⎰⎰ 例3.16．xdx ⎰4tan解：原式=dx x x x ]1)1(tan tan [tan 224++-+⎰=⎰⎰⎰+-+dx xdx dx x x 222sec )tan 1(tan =2tan tan tan xd x x x c -++⎰=31tan tan 3x x x c -++ 例3.17．dx x x x ⎰+-+22322 解：原式=dx x x ⎰+-+-1)1(5)1(22=222(1)15(1)1(1)1d x dx x x -+-+-+⎰⎰ =c x x x +-++-)1arctan(5)22ln(2例3.18．⎰解：原式==21(1)2x +-第三章不定积分1arcsin2xc-+例3.19．⎰+21x edx解：原式=dxeexxx⎰-+2221=222xxdex-⎰=cexx++-)1ln(22例例例例例2．直接交换法a）题型dxbaxf)(⎰+方法：令baxt+=，abtx)(2-=，2()f dx tf t dt a =⎰⎰ 例3.25．dx x ⎰+11 解：令2,t x x t ==， 原式=tdt t 211⎰+=⎰⎰+-122t dt dt =c t t ++-1ln 22=c x x ++-)1ln(22例3.26．⎰ 解：令1,12+=-=t x x t原式=22222211112(1)24(1)3(1)3(1)3t t dt dt d t dt t t t t t +-==+-++++++++⎰⎰⎰⎰=2ln(24)ln(3)t t C x C +++=++ 例3.27．dx xx ⎰+31 解：原式65236x tt t dt t t =+⎰=dt t t ⎰+163=⎰+-+-dt tt t )111(62 =c t t t t ++-+-)1ln(63223 =c x x x x ++-+-)1ln(632663 例3.28．dx e x ⎰+11解：原式2ln(1)t x t =-dt t t t ⎰-⋅1212 =⎰-dt t 1122=c t t ++-11ln =c e e x x +++-+)1111ln( b) 题型dx b ax f )(2⎰+f dx ⎰变换t a x sin =f dx ⎰ 变换t a x tan =第三章 不定积分f dx ⎰ 变换t a x sec =例3.29．dx xx ⎰-29 解：令3sin x t =，2例 例例原式231sec cos sin sec tdt tdt t c c t ===++⎰⎰ 例3.33．解：令1tan x t +=， 原式＝221sin cos sin cos sin cos t t dt dt t t t t -=+-⎰⎰＝22cos sin 12cos 12sin d t d t t t -+--⎰⎰＝||||C +（还原略）。

不定积分复习题及答案不定积分是微积分中的重要概念之一，它在求解函数的原函数时起到了关键作用。

通过对不定积分的复习，我们可以更好地理解和运用这一概念。

本文将通过一些典型的不定积分复习题，来帮助读者加深对不定积分的理解。

首先，我们来看一个简单的例子。

求解函数f(x) = 2x的不定积分。

根据不定积分的定义，我们可以将这个问题转化为求解函数F(x)，使得F'(x) = f(x)。

在这个例子中，我们可以很容易地得出F(x) = x^2 + C，其中C为常数。

这个结果告诉我们，函数f(x) = 2x的不定积分是F(x) = x^2 + C。

接下来，我们来看一个稍微复杂一些的例子。

求解函数f(x) = 3x^2 + 2x的不定积分。

同样地，我们可以通过求解函数F(x)，使得F'(x) = f(x)，来得到结果。

在这个例子中，我们可以使用不定积分的基本公式来求解。

根据不定积分的线性性质，我们可以将这个问题分解为求解3x^2的不定积分和求解2x的不定积分两部分。

首先，我们来求解3x^2的不定积分。

根据不定积分的幂函数积分公式，我们可以得到3x^2的不定积分是x^3 + C1，其中C1为常数。

接下来，我们来求解2x的不定积分。

根据不定积分的线性性质，我们可以得到2x的不定积分是x^2 + C2，其中C2为常数。

将这两部分的结果相加，我们可以得到函数f(x) = 3x^2 + 2x的不定积分是F(x) = x^3 + x^2 + C，其中C为常数。

这个结果告诉我们，函数f(x) = 3x^2 + 2x的不定积分是F(x) = x^3 + x^2 + C。

通过以上两个例子，我们可以看到不定积分的求解过程是通过找到函数F(x)，使得F'(x) = f(x)，来得到结果的。

在实际应用中，我们可以利用不定积分的基本公式和性质，来求解更加复杂的函数的不定积分。

除了基本的不定积分公式之外，还有一些特殊的不定积分需要我们注意。

江苏省 2017 年一般高校专转本选拔考试Part 1 Reading Comprehension (共20小题，每题 2 分，共 40 分 )Directions There are 4 passages in this part,Each passage is followed by some questions or unfinished statements,For each of them there are 4 choices marked A,B,C and D. You should decide on the best choiceand mark your answer by blackening the corresponding letter on Answer Sheet.We use both words and gestures to express our feelings,but the problem is that these words and gestures canbe understood in different waysIt is true that a smile means the same thing in any language,So does laughter or crying.There are also anumber of striking similarities in the way different animals show the same feelings .Dogs, tigers and humans，for example, often show their teeth when they are angry. This is probably because they are born with those behaviorpatternsFear is another emotion that is shown in much the same way all over the world. In Chinese and Englishliterature, a phrase like “ he wentpale and begin to tremble”suggests that the man is either very afraid or deepshocked, However, he”opened his eyes wide ”is used to suggest anger in Chinese whereas in English it meanssurprise In Chinese surprise can be described in a phrase li ke “ they stretched out their tongues” Sticking out you tongue in English is an insulting gesture or expresses strong dislikeEven in the same culture, people differ in ability to understand and express feelings,Experiments in Americahave shown that women are usually better than men at recognizing fear,anger,love and happiness on people ’ sfaces,Other studies show that older people usually find it easier to recognize or understand body language thanyounger people do.1.According to the passage，—— BA.We can hardly understand what people ’s gestures meanB.words and gestures may have different meaning in different culturesC.words can be better understood by older peopleD.gestures can be understood by most of the people while words cannot 2.People’s facial expressions may be misunderstood because——B A people of different ages may have different understandingB people have different culturesC people of different sexes may understand a gesture differentlyD people of different countries speak different languages3 .Even in the same culture. people —— AA. have different abilities to understand and express feelingsB.have exactly the same understanding of somethingC.never fail to understand each otherD.are equally intelligent4.From this passage, we can conclude —— CA words are used as frequently as gesturesB words are often difficult to understandC words and gestures are both used in expressing feelingsD gestures are more efficiently used than words5.The best title for this passage may be —— BA. Words and FeelingsB. Words,Gestures and FeelingsC.Gestures and FeelingsD.Culture and UnderstandingPassage TowQuestions 6 to 10 are based on the following passageThe English policeman has several nicknames but the most frequently used are"copper" and "bobby" the first name comes from the verb "to cop". (which is also slang).meaning to take or to capture". and the second comesfrom the first name of Sir Robert Peel, the nineteenth-century politician, who was the of the police force as we know it today. An early nickname for the policeman was "peeler" but this one has died out.Whatever we may call them,the general opinion of the police seems to be a favorable one, except, of course, among the criminal part of the community where the police are given more derogatory nicknames which originated in America, such as "fuzz" or "pig". Visitors to England seem to be very impressed by the English police. It has. Infact, become a standing joke that the Visitor to Britain, when asked tar his views of the country. will always say, at some point or other, "I think your policemen are wonderful."Well,the British bobby may not always be wonderful but he is usually a very friendly and helpful sort of character. A music-hall song of some years ago was called "If You Want To Know The Time, Ask A Policeman". Nowadays. most people own watches but they still seem to find plenty of other questions to ask the policemen.In London, the policemen spend so much of their time directing visitors about the city that one wonders how they ever find time to do anything else.Two things are Immediately noticeable to the stranger, when he sees an English policeman for the first time.The first is that he does not carry a pistol and the second is that he wears a very distinctive of headgear. the policeman's helmet ,His helmet, together which his height,enables an English policeman to he seen from a considerable distance, a fact that is not without its usefulness. From time to time it is suggested that the policeman should be given a pistol and that his helmetshould be taken from him, but both these suggestions are resisted by given and that his helmet should be taken from him ,but both suggestions are resisted by the majority of the public and the police themselves.6.Nowadays British people call the policeman —— CA.pigB. peelerC. BobbyD. Fuzz7. Which of the following statements is TRUE?BA. There are fewer criminals America than tn Britain.B. The English police usually leave a deep impression on visitors .C. The English bobby is friendly but not helpful.D. The English police enjoy having pistols.8. If you see an English policeman for the first time. you will probably notice at once that——CA. he often tells people timeB. he is usually very helpfulC.he has a helmet on the headD. he wears special clothes9. That an English policemen can be seen from some distance is —— DA.standing jokeB. Of no helpC. Strange and funnyD. Of some help10. Visitors praise the English police because —— AA. they are polite and helpfulB. they obey ordersC. they often given thanksD. they are armed with modem equipmentPassage ThreeQuestions 11 to 15 are based on the following passage.It is difficult to imagine what life would be like without memory. The meanings of thousands of everyday perceptions the bases for the decisions we make, and the roots of our habits and skills are to he found in our pastexperiences,which are brought into the present by memory.Memory can be defined as the capacity to keep information available for later use. It not only includes "remembering" things like arithmetic or historical facts but also involves any change in the way an animal typically behaves. Memory is involved when a rat gives up eating grain because he has sniffed something suspicious in the grain pile. Memory is also involved when a six-year-old child learns to swing a baseball bat.Memory exists not only in humans and animals but also in some physical objects and machines. Computers.for example, contain devices from storing data for later use. It is interesting to compare the memory-storage capacity of a computer with that of a human being. The instant-access memory of a large computer may hold up to 100,000"words" -ready for instant use. An average American teenager probably recognizes the meaning of about 100,000 words of English. However, this is but a fraction of the total amount of information which the teenager has stored. Consider. tar example- the number of faces and places that the teenager can recognize on sight.The use of words is the bass of the advanced problem-solving intelligence of human beings. A large part of a person's memory is in terms of words and combinations of words.11.According to the passage, memory is considered to be —— BA.the basis for decision making and problem solvingB.the ability to store information for future useC.an intelligence typically possessed by human beingsD.the data mainly consisting of words and combinations of words12.The comparison between the memory capacity of a large computer and that of a human being shows that——Cputer's memory has a little bigger capacity than a teenager'sputer's memory capacity is much smaller than an adult human being'sputer's memory's capacity is much smaller even than a teenager'sputer's memory's capacity is the same as a teenager's13.1t is implied in the passage that —— C14.The phrase “in terms of ”in the last sentence can be best replaced by—— BA.in connection withB. expressed byC.consistingD.by means of15.The main idea of the passage is—— BA.What life would be like without memoryB.Memory is of vital importance to lifeC.How a person ’s memory different from an animal ’s or a computer’sD.What memory carriesPassage fourQuestions 16 to 20 are based on the following passageClearly if we are to participate in the society in which we live, we must communicate with other people. Agreat deal of communicating is performed on a person-to-person basis by the simple means of speech. If we travelin buses, buy things in shops, or eat in restaurants, we are likely to have conversations where we give informationor opinions, receive news or comment, and very likely to have our views challenged by other members of society.Face to face contact is by no means the only form of communication and during the last two hundred years the art of mass communication has become one of the dominating factors of contemporary society. Two things, above others, have caused the enormous growth of the communication industry. Firstly, inventiveness has led to advanced imprinting, telecommunications photography, radio and television. Secondly, speed has revolutionized the transmission and reception of communications so that local news often takes a back seat to national news, which itself is often almost eclipsed( 相形见拙 ) by international news.No longer is the possession of information confined to( 只限于 ) a privileged minority. In the last century the wealthy man with his own library was indeed fortunate, but today there are public libraries. For years ago peopleused to flock to the cinema, but now far more people sit at home and turn on the TV to watch a programme that isbeing channeled into millions of homes.Communication is no longer merely concerned with the transmission of information. The modem communication industry influences the way people live in society and broadens their horizons by allowing accessto information, education and entertainment. The printing, broadcasting and advertising industries are all involved with informing, educating and entertaining.Although a great deal of the material communicated by the mass media is very valuable to the individual andto the society of which he is part, the vast modem network of communications is open to abuse. However, the mass media are with us for better, for worse, and there is no turning back.16.The first paragraph the writer emphasizes the—— of face-to-face contact in social setting.DA ． natureB ．limitation C． creativity D ．Usefulness17.The development of the communication industry in contemporary society results from—— BA.the advances and revolutionsB.the inventiveness and speedC.the art of mass communicationD.the advances and speed18.It is implied in the passage that—— C.A ． local news used to be the only source of informationB． local news still takes a significant placeC． national news is becoming more popularD． international news is the fastest transmitted news19.Which of the following statements is NOT true?AA ． Public libraries have replaced the private libraries.B． To possess information used to be a privilegeC． Communication means more than transmission.D． Communication influences ways of life and thinking.20.It can be inferred from the last paragraph we can infer that the writer is ___A___.A. concerned about the wrong use of the mass mediaB.Happy about the flexible change in the mass mediaC.Pessimistic about the future of the mass mediaD.Indifferent to the harmful influence of the mass medPart II Vocabulary and Structure (共 40 小题，每题 1 分，共 40 分)Directions : there are 40 incomplete sentences in this part For each sentence there are 4 choices marked A, B,C and D. Choose the ONE that best completes the sentence. Then mark your answer by blackening the corresponding letter on the Answer Sheet.21.I had supper with my friends yesterday afternoon._B___we went to attend a party.A.after whenB. after whichC. after thatD. after it查核：非限拟订语从句which ，本题在专转本英语中常考，有时直接which ，有时介词 +which.22. __A__ difficulties he comes across he can manage to get them over.A. WhateverB. WhicheverC. HoweverD. Wherever查核：疑问词 +ever 从前讲过叹息词中 what+名词； how+ 形容词，同理 whatever+名词， however+ 形容词。

江苏省专转本（高等数学）模拟试卷54(题后含答案及解析) 题型有：1. 选择题 2. 填空题 4. 解答题 5. 综合题 6. 证明题选择题在每小题给出的四个选项中，只有一项是符合要求的。

1．在下列的极限求解中，正确的是( )．A．B．C．D．正确答案：A解析：2．下列级数收敛的是( )．A．B．C．D．正确答案：D解析：选项A，很明显是一个发散级数(指数函数的增长速度高于幂函数增长速度)．B项用比较法通项发散，对于C，由于不存在，根据定义可知该级数发散，可排除D项，根据莱布尼兹判别法，单调下降，且．收敛，故此级数条件收敛．3．设a=一i+j+2k，b=3i+4k，用b0表示b方向上的单位向量，则向量a 在b上的投影为( )．A．B．b0C．D．一b0正确答案：B解析：根据矢量b在a上的投影公式4．设f(x)在x=x0处可导，则f’(x0)=( )．A．一4B．一2C．2D．4正确答案：B解析：5．函数的水平渐近线方程是( )．A．y=1B．y=2C．y=3D．y=0正确答案：C解析：=6.lne-3=6-3=3．6．下列不定积分计算正确的是( )．A．B．C．D．正确答案：A解析：填空题7．=____________.正确答案：解析：8．设f(x)为连续奇函数，则f(0)=___________．正确答案：0解析：(1)∵f(x)为奇函数，∴f(一x)=一f(x)，(2)，又f(x)在x=0连续，∴f(0)=一f(0)，故f(0)=0．9．=__________.正确答案：解析：10．已知则｜a+b｜=____________．正确答案：解析：｜a+b｜2=(a+b).(a+b)=｜a｜2+｜a｜2+2｜a｜｜b｜11．若直线y=5x+m是曲线y=x2+3x+2的一条切线，则常数m=___________．正确答案：1解析：由已知，切线斜率k=yt=2x+3—5，解得x=1，代入曲线方程得y=6，即切点坐标为(1，6)，代入切线方程y=5x+m，解得m=1．12．的定义域是_______．正确答案：D={(x，y)｜r2＜x2+y2＜R2)解析：∴定义域D={(x，y)｜r2＜x2+y2＜R2}．解答题解答时应写出推理、演算步骤。

江苏省专转本（高等数学）模拟试卷52(题后含答案及解析)题型有：1. 选择题 2. 填空题 4. 解答题 5. 综合题 6. 证明题选择题在每小题给出的四个选项中，只有一项是符合要求的。

1．函数在点x=0处( )．A．有定义但无极限B．无定义但有极限值0C．无定义但有极限值1D．既无定义又无极限值正确答案：B解析：无定义是显然的，因为极限(无穷小乘以有界量仍是无穷小)2．若f(x)在x=a处可导，则=( )．A．mf’(a)B．nf’(a)C．(m+n)f’(a)D．正确答案：C解析：在这里函数值由f(a一mh)变为f(a+nh)，自变量改变了(a+nh)一(a一mh)=(n+m)h，因此，相应地在分母的位置上构造出相同的自变量的改变量.3．设f(x)的导函数连续，且的一个原函数，则∫xf’(x)dx=( )．A．B．C．D．正确答案：D解析：因为是f(x)的一个原函数，所以有所以4．若f(x)在[一a，a]连续，则∫-aax[f(x)+f(-x)]dx=( )．A．2∫0axf(x)dxB．2∫0axf(一x)dxC．0D．2∫0ax[f(x)+f(-x)]dx正确答案：C解析：本题利用函数的对称性和奇偶性化简定积分计算，因为x[f(x)+f(一x)]为奇函数，所以结果为0．5．向量a=(1,-4,1)与b=(2,-2,-1)的夹角θ为( ).A．B．0C．D．正确答案：A解析：6．已知当x→0时，x2ln(1+x2)是sinnx的高阶无穷小，而sinnx又是1一cosx的高阶无穷小，则正整数n=( )．A．1B．2C．3D．4正确答案：C解析：由已知，则n＜4，又sinnx是1一cosx 的高阶无穷小，则．则n＞2，所以n=3，选C项．填空题7．若且f(x)在x=x0处有定义，则当A=________时，f(x)在x=x0处连续．正确答案：f(x0)解析：根据连续的定义，，所以A=f(x0)时，f(x)在x=x0处连续．8．的水平渐近线是__________，垂直渐近线是_________．正确答案：y=1，x=1解析：是其水平渐近线．．是其垂直渐近线．9．=__________.正确答案：解析：设x=asect，dx=asecttantdt，换限：当x=a时，t=0；当x=2a时，于是10．设向量a=(2，4，一5)，b=(2，3，k)，若a与b垂直，则k=________．正确答案：解析：11．二次积分∫01dx∫0x24xdy=__________．正确答案：1解析：12．交换积分的次序：∫1edx∫0lnxf(x，y)dy=_________．正确答案：∫10dy∫eeyf(x,y)dx解析：画出积分区域D：1≤x≤e，0≤y≤lnx，见图改写D：0≤y≤1，ey≤x≤e便得原式=∫01dy∫eyef(x，y)dx.解答题解答时应写出推理、演算步骤。

江苏省2017年普通高校专转本选拔考试Part 1 Reading Comprehension (共20小题，每小题2分，共40分)Directions There are 4 passages in this part,Each passage is followed by some questions or unfinished statements,For each of them there are 4 choices marked A,B,C and D. You should decide on the best choice and mark your answer by blackening the corresponding letter on Answer Sheet.Passage OneQuestions 1 to 5 are based on the following passageWe use both words and gestures to express our feelings,but the problem is that these words and gestures can be understood in different waysIt is true that a smile means the same thing in any language,So does laughter or crying.There are also a number of striking similarities in the way different animals show the same feelings .Dogs, tigers and humans，for example, often show their teeth when they are angry. This is probably because they are born with those behavior patternsFear is another emotion that is shown in much the same way all over the world. In Chinese and English literature, a phrase like “he went pale and begin to tremble” suggests that the man is either very afraid or deep shocked, However,” he opened his eyes wide” is used to suggest anger in Chinese whereas in English it means surprise In Chinese surprise can be described in a phrase li ke “they stretched out their tongues” Sticking out your tongue in English is an insulting gesture or expresses strong dislikeEven in the same culture, people differ in ability to understand and express feelings,Experiments in America have shown that women are usually better than men at recognizing fear,anger,love and happiness on people’s faces,Other studies show that older people usually find it easier to recognize or understand body language than younger people do.1.According to the passage，——BA.We can hardly understand what people’s gestures meanB.words and gestures may have different meaning in different culturesC.words can be better understood by older peopleD.gestures can be understood by most of the people while words can not2.People’s facial expressions may be misunderstood because——BA people of different ages may have different understandingB people have different culturesC people of different sexes may understand a gesture differentlyD people of different countries speak different languages3 .Even in the same culture. people ——AA.have different abilities to understand and express feelingsB.have exactly the same understanding of somethingC.never fail to understand each otherD.are equally intelligent4.From this passage, we can conclude ——CA words are used as frequently as gesturesB words are often difficult to understandC words and gestures are both used in expressing feelingsD gestures are more efficiently used than words5.The best title for this passage may be ——BA.Words and FeelingsB.Words,Gestures and FeelingsC.Gestures and FeelingsD.Culture and UnderstandingPassage TowQuestions 6 to 10 are based on the following passageThe English policeman has several nicknames but the most frequently used are"copper" and "bobby" the first name comes from the verb "to cop". (which is also slang).meaning to take or to capture". and the second comes from the first name of Sir Robert Peel, the nineteenth-century politician, who was the of the police force as we know it today. An early nickname for the policeman was "peeler" but this one has died out.Whatever we may call them,the general opinion of the police seems to be a favorable one, except, of course, among the criminal part of the community where the police are given more derogatory nicknames which originated in America, such as "fuzz" or "pig". Visitors to England seem to be very impressed by the English police. It has. In fact, become a standing joke that the Visitor to Britain, when asked tar his views of the country. will always say, at some point or other, "I think your policemen are wonderful."Well,the British bobby may not always be wonderful but he is usually a very friendly and helpful sort of character. A music-hall song of some years ago was called "If You Want To Know The Time, Ask A Policeman". Nowadays. most people own watches but they still seem to find plenty of other questions to ask the policemen. In London, the policemen spend so much of their time directing visitors about the city that one wonders how they ever find time to do anything else.Two things are Immediately noticeable to the stranger, when he sees an English policeman for the first time. The first is that he does not carry a pistol and the second is that he wears a very distinctive of headgear. the policeman's helmet ,His helmet, together which his height,enables an English policeman to he seen from a considerable distance, a fact that is not without its usefulness. From time to time it is suggested that the policeman should be given a pistol and that his helmetshould be taken from him, but both these suggestions are resisted by given and that his helmet should be taken from him ,but both suggestions are resisted by the majority of the public and the police themselves.6.Nowadays British people call the policeman ——CA.pigB. peelerC. BobbyD. Fuzz7. Which of the following statements is TRUE? BA. There are fewer criminals America than tn Britain.B. The English police usually leave a deep impression on visitors.C. The English bobby is friendly but not helpful.D. The English police enjoy having pistols.8. If you see an English policeman for the first time. you will probably notice at once that ——CA. he often tells people timeB. he is usually very helpfulC.he has a helmet on the headD. he wears special clothes9. That an English policemen can be seen from some distance is ——DA.standing jokeB. Of no helpC. Strange and funnyD. Of some help10. Visitors praise the English police because ——AA.they are polite and helpfulB. they obey ordersC. they often given thanksD. they are armed with modem equipmentPassage ThreeQuestions 11 to 15 are based on the following passage.It is difficult to imagine what life would be like without memory. The meanings of thousands of everyday perceptions the bases for the decisions we make, and the roots of our habits and skills are to he found in our pastexperiences,which are brought into the present by memory.Memory can be defined as the capacity to keep information available for later use. It not only includes "remembering" things like arithmetic or historical facts but also involves any change in the way an animal typically behaves. Memory is involved when a rat gives up eating grain because he has sniffed something suspicious in the grain pile. Memory is also involved when a six-year-old child learns to swing a baseball bat.Memory exists not only in humans and animals but also in some physical objects and machines. Computers. for example, contain devices from storing data for later use. It is interesting to compare the memory-storage capacity of a computer with that of a human being. The instant-access memory of a large computer may hold up to 100,000" words" -ready for instant use. An average American teenager probably recognizes the meaning of about 100,000 words of English. However, this is but a fraction of the total amount of information which the teenager has stored. Consider. tar example- the number of faces and places that the teenager can recognize on sight.The use of words is the bass of the advanced problem-solving intelligence of human beings. A large part of a person's memory is in terms of words and combinations of words.11.According to the passage, memory is considered to be ——BA.the basis for decision making and problem solvingB. the ability to store information for future useC. an intelligence typically possessed by human beingsD. the data mainly consisting of words and combinations of words12.The comparison between the memory capacity of a large computer and that of a human being shows that——Cputer's memory has a little bigger capacity than a teenager'sB. computer's memory capacity is much smaller than an adult human being'sC. computer's memory's capacity is much smaller even than a teenager'sD. computer's memory's capacity is the same as a teenager's13.1t is implied in the passage that ——CA. only human beings have problem-solving intelligenceB a person's memory is different from a computer's in every respectC. animals can solve very simple problemsD animals solve problems by instincts rather than intelligence14.The phrase “in terms of”in the last sentence can be best replaced by——BA.in connection withB.expressed byC.consistingD.by means of15.The main idea of the passage is——BA.What life would be like without memoryB.Memory is of vital importance to lifeC.How a person’s memory different from an animal’s or a computer’sD.What memory carriesPassage fourQuestions 16 to 20 are based on the following passageClearly if we are to participate in the society in which we live, we must communicate with other people. A great deal of communicating is performed on a person-to-person basis by the simple means of speech. If we travel in buses, buy things in shops, or eat in restaurants, we are likely to have conversations where we give information or opinions, receive news or comment, and very likely to have our views challenged by other members of society.Face to face contact is by no means the only form of communication and during the last two hundred years the art of mass communication has become one of the dominating factors of contemporary society. Two things, above others, have caused the enormous growth of the communication industry. Firstly, inventiveness has led to advanced imprinting, telecommunications photography, radio and television. Secondly, speed has revolutionized the transmission and reception of communications so that local news often takes a back seat to national news, which itself is often almost eclipsed( 黯然失色) by international news.No longer is the possession of information confined to(只限于) a privileged minority. In the last century the wealthy man with his own library was indeed fortunate, but today there are public libraries. For years ago people used to flock to the cinema, but now far more people sit at home and turn on the TV to watch a programme that is being channeled into millions of homes.Communication is no longer merely concerned with the transmission of information. The modem communication industry influences the way people live in society and broadens their horizons by allowing access to information, education and entertainment. The printing, broadcasting and advertising industries are all involved with informing, educating and entertaining.Although a great deal of the material communicated by the mass media is very valuable to the individual and to the society of which he is part, the vast modem network of communications is open to abuse. However, the mass media are with us for better, for worse, and there is no turning back.16.The first paragraph the writer emphasizes the ——of face-to-face contact in social setting. DA．nature B．limitation C．creativity D．Usefulness17.The development of the communication industry in contemporary society results from ——BA.the advances and revolutionsB.the inventiveness and speedC.the art of mass communicationD.the advances and speed18.It is implied in the passage that —— C .A．local news used to be the only source of informationB．local news still takes a significant placeC．national news is becoming more popularD．international news is the fastest transmitted news19.Which of the following statements is NOT true? AA．Public libraries have replaced the private libraries.B．To possess information used to be a privilegeC．Communication means more than transmission.D．Communication influences ways of life and thinking.20.It can be inferred from the last paragraph we can infer that the writer is ___A___.A.concerned about the wrong use of the mass mediaB.Happy about the flexible change in the mass mediaC.Pessimistic about the future of the mass mediaD.Indifferent to the harmful influence of the mass medPart II Vocabulary and Structure (共40小题，每小题1分，共40分)Directions : there are 40 incomplete sentences in this part For each sentence there are 4 choices marked A, B, C and D. Choose the ONE that best completes the sentence. Then mark your answer by blackening the corresponding letter on the Answer Sheet.21.I had supper with my friends yesterday afternoon._B___we went to attend a party.A.after whenB. after whichC. after thatD. after it考核：非限制定语从句which，此题在专转本英语中常考，有时候直接which，有时候介词+which.22. __A__ difficulties he comes across he can manage to get them over.A. WhateverB. WhicheverC. HoweverD. Wherever考核：疑问词+ever 之前讲过感叹词中what+名词；how+形容词，同理whatever+名词，however+形容词。

江苏省专转本高等数学模拟测试题一．选择题(每小题4分,共24分) 1.当 0x→时, 1cos 2x -与2ln(1)ax +是等价无穷小，则常数a 的值为( )A. 1B. 2C.3D. 4解：本题考查无穷小阶的比较，就是求两个函数比值的极限，条件说是等价无穷小，那么比值的极限是1，即有222001(2)1cos 222lim lim 1ln(1)x x x x ax ax a→→-===+ 则2a=，选B 。

2.曲线2(1)(2)x xy x x x -=--的垂直渐近线是( )A.0x = B. 1x = C. 2x = D. 没有垂直渐近线解：所谓垂直渐近线就是若0lim ()x xf x →=∞（也可以是单侧极限，即左极限或右极限为无穷大），则称0x x =为垂直渐近线。

一般拿来讨论极限的0x 为函数中无定义的点，本题有三个无定义的点，即0x =，1x =，2x =，但是在求极限时函数经过化简后变成12y x =-，因此只有21lim2x x →=∞-，所以选C 。

3. 设sin 0()ln(1)xx t t dt ϕ=+⎰，则()x ϕ'=( )A. sin cos ln(1sin )x x x +B. sin ln(1sin )x x +C. sin cos ln(1sin )x x x -+D. sin ln(1sin )x x -+ 解：本题考查变上限积分函数求导公式，选A 。

4. 下列级数中条件收敛的是( )A.21(1)nn n∞=-∑ B.1(1)1nn n ∞=-+∑ C.11(1)21nn n n ∞=+-+∑ D.1(1)2nnn ∞=-∑解：本题考查绝对收敛与条件收敛的概念，首先要知道无论是绝对收敛还是条件收敛都是满足收敛，只是收敛的“强度”不同罢了。

选项A 与D 都是满足绝对收敛的，选项C 一般项的极限不是零，显然发散，只有选项B 满足条件收敛。

5.将二重积分D⎰⎰，{(,)|1}D x y x y x =≤≤≤≤化成极坐标下的二次积分，则得( )A.224d r drπθ⎰⎰B.240d dr πθ⎰C. 2224d r dr ππθ⎰⎰D. 2204d dr ππθ⎰解： 本题考查二重积分的极坐标变换，首先关键是画出积分区域来，作图如下： 本题积分区域形如右图阴影部分，显然答案选D 。

同方专转本高等数学核心教程第三章不定积分本章主要知识点：● 不定积分的意义，基本公式● 不定积分的三种基本方法● 杂例历年考试真题1.（2001）不定积分=（ D ）A.B. +CC. arcsinxD. arcsinx+C解析: 利用不定积分的定义.2001）计算⎰e2x2. （1+exdx。

解: ⎰e2xe2x+ex-exx1+exdx=⎰1+exdx=e-ln(1+ex)+C3. （2002）设f(x)有连续的导函数，且a≠0,1，则下列命题正确的是（A. ⎰f'(ax)dx=1af(ax)+C B. ⎰f'(ax)dx=f(ax)+CC. (⎰f'(ax)dx)'=af(ax)D. ⎰f'(ax)dx=f(x)+C解析: 由⎰f'(x)dx=f(x)+C⎰f'(ax)dx=1a⎰f'(ax)dax=1af(ax)+C4. （2002）求积分2解: 14arcsin2x2+C5. （2003）若F'(x)=f(x),f(x)连续，则下列说法正确的是（ C ） - 78 - A ）第三章不定积分A.C. ⎰F(x)dx=f(x)+c B. ⎰⎰dF(x)dx=f(x)dx dx⎰dF(x)dx=f(x) f(x)dx=F(x)+c D. dx⎰解析: 不定积分的定义 6. （2003）xlnxdxx2x2x2=lnx-⎰dlnx 解: 设u=lnx,dv=xdx,则⎰xlnxdx=⎰lnxd222x21=lnx-⎰xdx22 11=x2(lnx-)+C227. （2004）求不定积分3=1arcsin4x+C 4解析: 31dx=⎰arcsin3xdarcsinx=arcsin4x+C 4ex8. （2004）设f(x)的一个原函数为，计算⎰xf'(2x)dx xexex(x-1)ex解: 因为f(x)的一个原函数为，所以f(x)=()'=， xx2x1111⎰xf'(2x)dx=⎰xf'(2x)d(2x)=⎰xdf(2x)=xf(2x)-⎰f(2x)dx 222211x(2x-1)e2xx-12x-+C=e+C ＝xf(2x)-⎰f(2x)d(2x)=248x28x4x9. （2005）若⎰f(x)dx=F(x)+C,则⎰sinxf(cosx)dx=( D )A. F(sinx)+CB. -F(sinx)+CC. F(cosx)+CD. -F(cosx)+C解析: ⎰sinxf(cosx)dx=-⎰f(cosx)dcosx=-F(cosx)+C⎰310. （2005）计算tanxsecxdx2 解：原式＝tanxtanxsecxdx=⎰⎰(secx-1)d- 79 - 22secx=⎰secxdsecx-secx同方专转本高等数学核心教程=secx-secx+C11.（2006）已知A.2e-2x133⎰f(x)dx=e2x+C，则⎰f'(-x)dx=（ C ）. 11+CB.e-2x+CC. -2e-2x+CD. -e-2x+C 22解析: 由题意f(x)=2e2x,∴f'(x)=4e2x,f'(-x)=4e-2x所以⎰f'(-x)dx=⎰4e-2x-2xdx=⎰-2e-2xd(-2x)=-2e+C12.（2006）计算⎰dx x解：原式＝32(1+lnx)=(1+lnx)2+C 313. (2007) 设函数f(x)的一个原函数为sin2x，则⎰f'(2x)dx=（ A ）1cos4x+C 2C. 2cos4x+CD. sin4x+C A. cos4x+C B.解析: f(x)=2cos2x,所以f'(x)=4sin2x,⎰f'(2x)dx=⎰4sin4xdx=⎰sin4xd(4x)=cos4x+C2-x14. (2007)求不定积分xedx．⎰2-x2-x 解：xedx=-xd(e) ⎰⎰2-x-x2-x-x =-xe+2xedx=-xe-2xd(e) ⎰⎰2-x-x-x =-xe-2xe+2edx ⎰=-xe单元练习题3 2-x-2xe-x-2e-x+C1．dcos2x=- 80 - ⎰第三章不定积分2．已知f(cosx)=sin2x，则⎰f(x-1)dx=。

第三章 不定积分本章主要知识点：12 （2）c aa dx a x x+=⎰ln ，c e dx e x x +=⎰ （3）⎰+-=c x xdx cos sin ，⎰+=c x xdx sin cos ，c x xdx +=⎰tan sec 2，c x xdx +-=⎰cot csc 2（4）c a xdx x a +=-⎰arcsin 122，（5）c x a xa a dx x a +-+=-⎰||ln 21122121111f dx f d x x x x ⎛⎫⎛⎫⎛⎫=- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎰⎰ ⎰⎰=x d x f dx x xf tan )(tan )(tan sec 2tan sec (sec )(sec )sec x xf x dx f x d x =⎰⎰ 等等。

例3.1．22007(21)x x dx +⎰解：原式=2200722200811(21)(21)(21)48032x d x x c ++=++⎰ 例3.2．3sin 13sin 13sin 111cos (3sin 1)33x x x xedx e d x e c ---=-=+⎰⎰ 例23例例例例14C +例3.8．⎰+dx exe x解：原式xxxe xe xe e e dx e de e C =⋅==+⎰⎰例3.9．⎰+++dx x x x 2233 解：利用综合除法知12127222323+-+-=+++x x x x x x原式C x x x x dx x x x ++-+-=+-+-=⎰2ln 12731)21272(232例 例例=x C =+例3.13．sin sin cos xdx x x +⎰解：原式=1(sin cos sin cos )2sin cos x x x x dx x x ++-⋅+⎰=11(cos sin )22sin cos d x x dx x x --++⎰⎰=11ln sin cos 22x x x c +++例例例 例 例3.18．解：原式==21(1)2x +-1arcsin2xc-+例3.19．⎰+21x edx解：原式=dxeeexxx⎰+-+22211=2221xxdexe-+⎰=cexx++-)1ln(22例例例例例2．直接交换法a）题型dxbaxf)(⎰+方法：令baxt+=，abtx)(2-=，2()f dx tf t dta=⎰⎰例3.25．dxx⎰+11解：令2,txxt==，例=例例b) 题型dxbaxf)(2⎰+f dx⎰变换tax sin=f dx⎰变换tax tan=f dx ⎰变换t a x sec =例3.29．dx xx ⎰-29 解：令3sin x t =，2例 例例原式231sec cos sin sec tdt tdt t c c t ===++⎰⎰ 例3.33．解：令1tan x t +=，原式＝221sin cos sin cos sin cos t t dt dt t t t t -=+-⎰⎰＝22cos sin 12cos 12sin d t d tt t -+--⎰⎰＝|C +（还原略）。