2022年396經(jīng)濟(jì)類聯(lián)考-數(shù)學(xué)真題

1、2022 年 396 經(jīng)濟(jì)類聯(lián)考-數(shù)學(xué)真題一單項(xiàng)選擇題(共 35 題，每題 2 分，共 70 分)21. lim x sin = ( E)x) -w xA. - 21B. - 2C.01D. 2E.22.設(shè)a, b為實(shí)數(shù)，lim 3x2 + ax + b = 4,則( B)x) - 1 x +1A.a = 7,b = 4B.a = 10,b = 7C.a = 4,b = 7D.a = 10,b = 6E.a = 2,b = 3)3.已知a, b為實(shí)數(shù)，且a 豐 0,函數(shù)f (x) =1- exaxb,x, 0 在x = 0處連續(xù)，則ab = (EA.2B.11C. 2D.0E. - 14.已知

2、函數(shù)f (x) = 1+ x - 1,g(x) = ln , h(x) = 2x - 1,w(x) = sin2 (x)x,在x ) 0時(shí)，與x等價(jià)的無(wú)窮小是(A )A.g(x), w(x)B.f (x), h(x)C.g(x), h(x)D.f (x), g(x)E.h(x), w(x)5.曲線y = x x (0 共 x 共 4)的長(zhǎng)度為(D3A.14B.167C. 256D. 964E. 96.已知f (x)可導(dǎo)， f (0) = 1,f (0) = -1,則lim 3x (1- f (x) = ( B)x)0 xA. - 1 B.1C. - ln 3 D.ln 3 E.07.已知函數(shù)f

3、 (x)可導(dǎo)且f (0) = 3,設(shè)g(x) = f (4x2 + 2x)，則dg = (E )x=0A.0B.2dxC.3dxD.4dxE.6dx(sin x8.已知函數(shù)f (x) =|lx1,x, 0 , 則f (0) + f (1)= (A )A.cos1 - sin1B.sin1 - cos1C.cos1 + sin1D.1+ cos1 - sin1E.1+ sin1 - cos19.設(shè)函數(shù)y = f (x)由y + xexy = 1確定，則曲線y = f (x)在點(diǎn)(0，f (0)處的切線方程是( A)A.x + y = HYPERLINK l _bookmark1 1B.x + y

4、 = -1C.x - y = 1D.x - y = -1E.2x + y = 1e10.函數(shù)f (x) = (x2 3)ex 的( B)A.最大值是6e3B.最小值是-2eC.遞減區(qū)間是(- ,0)D.遞增區(qū)間是(0，+)E.凹區(qū)間是(0，+)11.設(shè)連續(xù)函數(shù)f (x)滿足j 2x f (t)dt = ex 1,則f (1)= ( E)0A.eB. 2C. eD. 2ee2E. 212.設(shè)I = j esin x cos2 xdx, J = j esin x cos3 xdx, K = j esin x cos4 xdx, 則(E )0 0 0A.I J KB.K J IC.K I JD.J

5、I KE.J K I1 1A)13.j 1 ex dx = (1 x3 2A.e2B. e2eC.2D.2e eE.3e2 2e14.設(shè)函數(shù)f (x)的一個(gè)原函數(shù)是x sin x, j xf (x)dx = (C0A.0)B.1C. D.E.2C)15.已知變量y關(guān)于x的變化率等于+1,當(dāng)x從1變到9時(shí)， y的改變量是(A.8B.10C.12D.14.E.1616.設(shè)平面有界區(qū)域D由曲線y = sin x(0 共 x 共 2幾)與x軸圍成，則D繞x軸旋轉(zhuǎn)所成旋轉(zhuǎn)體體積為(D )幾A. 2B.幾幾 2C. 2D.幾 2 E.4幾17.設(shè)非負(fù)函數(shù)f (x)二階可導(dǎo)，且f (x) 0,則(A )A.

6、j2 f (x)dx f (0) + f ( HYPERLINK l _bookmark2 2)0B.j2 f (x)dx f (0) + f (1)0C.j2 f (x)dx f (0) + f (2)E.2f (1)= f (0) + f (2)?x (0,1) ?y (0,1)18.已知函數(shù)f (u)可導(dǎo)，設(shè)z=f (y - x) + sin x + ey , 則?z + ?z = (B )A.1B.e +1C.e - 1D.幾 - eE.幾 + e( x y| ,( x, y) 豐 (0,0)19.已知函數(shù)f (x, y) =| x2 + y2 在點(diǎn)(0,0)處，給出下列結(jié)論l 0,(

7、 x, y) = (0,0)?x ?y ?x ?y(1)f (x, y)連續(xù)(2) ?f 存在，?f 不存在 (3) ?f =0，?f =0 (4) df=0其中所有正確結(jié)論的序號(hào)是(D )A.(1)B.(2)C.(1)(2)D.(1)(3)E.(1)(3)(4)20.已知函數(shù)f (x, y) = x2 + 2y2 + 2xy + x + y, 則( C)1A.f (一 ,0)是極大值 21B.f (0, )是極大值 21C.f (一 ,0)是極小值 21D.f (0, 一 )是極小值 2E.f (0,0)是極小值21.已知函數(shù)f (u, v)具有二階連續(xù)偏導(dǎo)數(shù)，且?f = 2,?2 f =

8、3,?v (0,1) ?u2 (0,1)設(shè)g(x)=f (sin x,cos x),則d 2 g = (A )dx2 x=0A.1B.2C.3D.4E.522.設(shè) 11 12 = M , 11 12 = N, 則(B )a a b b21 22 21 22A.當(dāng)a = 2b (i, j = 1,2)時(shí)， M = 2Nij ijB.當(dāng)a = 2b (i, j = 1,2)時(shí)， M = 4Nij ijC.當(dāng)M = N時(shí)， a = b (i, j = 1,2)ij ijD.當(dāng)M = 2N時(shí)， a = 2b (i, j = 1,2)ij ijE.當(dāng)M = 4N時(shí)， a = 2b (i, j = 1,2

9、)ij ij 1 一2 1 a a b b 23.已知f (x) = 一1 4 x , 則f (x) = 0的根為(E )1 一8 x2A.x = 一1,x = 11 2B.x = 1,x = 一21 2C.x = 1,x = 21 2D.x = 一1,x = 21 2E.x = 一1,x = 一21 2( a a )24.設(shè)A = | 11 12 | , 其中a =1,2,3(i, j = 1,2).若對(duì)A施以交換兩行(a a ) ij21 22的初等變換，再施以交換兩列的初等變換，得到的矩陣仍為A, 則這樣的 矩陣共有(D )A.3個(gè)B.4個(gè)C.6個(gè)D.9個(gè)E.12個(gè)0 0 1a a 31

10、 3225. | | = (C )12 11 12A. a + ka a 11 12 12B. |a a + ka 11 12 11C. |a a + ka 11 11 12D. |a + ka a + ka 11 12E. |26.已知a ，a ，a ，a 是3維向量組，若向量組a +a ，a +a ，a +a1 2 3 4 1 2 2 3 3 4線性無(wú)關(guān)，則向量組(D )A.0B.1C.2D.3E.427.設(shè)k為實(shí)數(shù)，若向量組(1,3,1)， (-1，k,0),( -k, 2, k)線性相關(guān)，則k = (B )1A. - 2或- 21B. - 2或 21C.2或- 21D.2或 2E.2或

11、-2(a 1 1 28.設(shè)矩陣A = | ,(1)當(dāng)a = 1時(shí)， Ax = 0的基礎(chǔ)解系中含有1個(gè)向量(2)當(dāng)a = -2時(shí)， Ax = 0的基礎(chǔ)解系中含有1個(gè)向量(3)當(dāng)a = 1時(shí)， Ax = 0的基礎(chǔ)解系中含有2個(gè)向量(4)當(dāng)a = -2時(shí)， Ax = 0的基礎(chǔ)解系中含有2個(gè)向量其中所有正確結(jié)論的序號(hào)是(D )A.(1)B.(2)C.(1)(2)D.(2)(3)E.(3)(4) 0, x 11 X 1),(2e-2x , x 0b = P(X 20 X 10), c = P(X 100X 90),則( D)A.a b cB.a = c bC.c a = bD.a = b = cE.b a = c1 231.設(shè)隨機(jī)變量X , Y獨(dú)立同分布， P(X = 0) = , P(X = 1) = ,3 3則P(XY = 0) = (C )A.04B. 95C. 92D. 37E. 91 1 132.已知隨機(jī)事件A, B滿足P(B A) = , P(A B) = , P(AB) = ,2 3 8則P(A B) = ( C)1A.43B.81C.25D.83E.433.設(shè)隨機(jī)變量X 服從正態(tài)分布， X N(2,9), 若P(X 1)= a,則P(X 5) =( D)A.1-a1B.