江蘇今年專升本數(shù)學(xué)試卷一、選擇題（每題1分，共10分）

1.函數(shù)f(x)=|x|在x=0處的導(dǎo)數(shù)是（）

A.0B.1C.-1D.不存在

2.極限lim(x→∞)(3x^2+2x+1)/(5x^2-3x+4)的值是（）

A.0B.1/5C.3/5D.∞

3.曲線y=x^3-3x^2+2在x=1處的切線斜率是（）

A.-1B.0C.1D.2

4.函數(shù)f(x)=e^x在區(qū)間[0,1]上的平均值是（）

A.eB.e-1C.1D.1/e

5.級數(shù)∑(n=1to∞)(-1)^(n+1)/n的和是（）

A.0B.1C.ln2D.π

6.微分方程y''-4y=0的通解是（）

A.y=C1e^2x+C2e^-2xB.y=C1x+C2x^2

C.y=C1sin2x+C2cos2xD.y=C1e^x+C2e^-x

7.函數(shù)f(x)=x^2在區(qū)間[1,2]上的定積分是（）

A.3B.4C.5D.6

8.矩陣A=[[1,2],[3,4]]的行列式det(A)是（）

A.-2B.-1C.1D.2

9.設(shè)向量a=(1,2,3)，向量b=(4,5,6)，則向量a和向量b的夾角cosθ是（）

A.1/2B.1/3C.2/3D.3/4

10.圓柱體的體積公式是（）

A.πr^2hB.2πrhC.πr^2D.2πr

二、多項(xiàng)選擇題（每題4分，共20分）

1.下列函數(shù)中，在x=0處可導(dǎo)的有（）

A.f(x)=x^2B.f(x)=|x|C.f(x)=sinxD.f(x)=log(x+1)

2.極限lim(x→0)(sinx)/x的值是（）

A.0B.1C.∞D(zhuǎn).不存在

3.下列級數(shù)中，收斂的有（）

A.∑(n=1to∞)1/n^2B.∑(n=1to∞)1/nC.∑(n=1to∞)(-1)^n/nD.∑(n=1to∞)1/n^3

4.微分方程y'+y=0的通解是（）

A.y=Ce^-xB.y=CsinxC.y=CcosxD.y=Ce^x

5.下列矩陣中，可逆的有（）

A.[[1,0],[0,1]]B.[[1,2],[2,4]]C.[[3,0],[0,3]]D.[[0,1],[1,0]]

三、填空題（每題4分，共20分）

1.函數(shù)f(x)=x^3-3x^2+2在x=2處的導(dǎo)數(shù)f'(2)=______。

2.極限lim(x→3)(x^2-9)/(x-3)=______。

3.曲線y=e^x在點(diǎn)(0,1)處的切線方程是______。

4.若函數(shù)f(x)在區(qū)間[a,b]上連續(xù)，則在(a,b)內(nèi)至少存在一點(diǎn)ξ，使得f(ξ)=______。

5.矩陣A=[[1,2],[3,4]]的特征值是______和______。

四、計算題（每題10分，共50分）

1.計算不定積分∫(x^2+2x+1)/(x+1)dx。

2.求極限lim(x→0)(e^x-1-x)/(x^2)。

3.計算定積分∫[0,π/2]sin^2xdx。

4.解微分方程y'-y=e^x。

5.求解線性方程組：

x+2y+3z=1

2x+5y+7z=4

3x+4y+8z=7。

本專業(yè)課理論基礎(chǔ)試卷答案及知識點(diǎn)總結(jié)如下

一、選擇題答案

1.A

2.C

3.A

4.B

5.C

6.A

7.A

8.A

9.B

10.A

二、多項(xiàng)選擇題答案

1.A,C

2.B

3.A,C,D

4.A

5.A,C,D

三、填空題答案

1.f'(2)=3(2)^2-3(2)=6-6=0

2.lim(x→3)(x^2-9)/(x-3)=lim(x→3)(x+3)(x-3)/(x-3)=lim(x→3)(x+3)=6

3.y-1=e^0(x-0)=>y-1=x=>y=x+1

4.(b-a)f(a)

5.特征值：λ1=5,λ2=-1

四、計算題答案及過程

1.∫(x^2+2x+1)/(x+1)dx=∫(x+1)^2/(x+1)dx=∫(x+1)dx=∫xdx+∫1dx=x^2/2+x+C

2.lim(x→0)(e^x-1-x)/(x^2)=lim(x→0)(e^x-1-x)/x^2*x/x=lim(x→0)(e^x-1-x)/x*1/x=lim(x→0)(e^x-1)/x-1/x=1-1=0

3.∫[0,π/2]sin^2xdx=∫[0,π/2](1-cos2x)/2dx=1/2∫[0,π/2](1-cos2x)dx=1/2[x-sin2x/2]from0toπ/2=1/2[(π/2)-0]=π/4

4.y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x=>y'=y+e^x=>y'-y=e^x