1、最新试题库含答案高等数学基础形成性考核册答案2016年7月高等数学基础形成性考核册答案 :篇一:高等数学基础形成性考核册及答案高等数学基础第一次作业第1章 函数第2章 极限与连续(一)单项选择题下列各函数对中,( C )中的两个函数相等2 A. f(x)?(x),g(x)?x B. f(x)?x2,g(x)?xx2?1 C. f(x)?lnx,g(x)?3lnxD. f(x)?x?1,g(x)? x?1设函数f(x)的定义域为(?,?),则函数f(x)?f(?x)的图形关于(C)对称 3A. 坐标原点 B. x轴C. y轴D. y?x下列函数中为奇函数是( B )A. y?ln(1?x)B.
2、y?xcosx 2ax?a?xC. y?D. y?ln(1?x) 2下列函数中为基本初等函数是(C)A. y?x?1 B. y?xC. y?x2 D. y?1,x?0 1,x?0?下列极限存计算不正确的是( D )x2?1B. limln(1?x)?0A. lim2x?0x?x?2sinx1 C. lim?0 D. limxsin?0 x?x?xx当x?0时,变量( C )是无穷小量1sinx A.B. xx1 C. xsin D. ln(x?2) x若函数f(x)在点x0满足( A ),则f(x)在点x0连续。A. limf(x)?f(x0)B. f(x)在点x0的某个邻域内有定义 x?x0
3、C. lim?f(x)?f(x0)D. lim?f(x)?lim?f(x) x?x0x?x0x?x0(二)填空题x2?9?ln(1?x)的定义域是函数f(x)?x?322 已知函数f(x?1)?x?x,则f(x)?1x1/ 2 lim(1? )?x?2x1?x? 若函数f(x)?(1?x),x?0,在x?0处连续,则k? e?x?0?x?k,?x?1,x?0 函数y?的间断点是 ?sinx,x?0若limf(x)?A,则当x?x0时,f(x)?A称为 x?x0(三)计算题设函数?ex,f(x)?x,求函数y?lglgx?0x?0 求:f(?2),f(0),f(1) 解:f(-2) = - 2,
4、f(0) = 0, f(1) = e 2x?1的定义域 x2x?1 解:由?0解得x 0或x 1/2,函数定义域为(-,0)(1/2,+) x在半径为R的半圆内内接一梯形,试将梯形的面积表示成其高的函数解:如图梯形面积A=(R+b)h,其中b? 22 R2?h2 A?(R?R?h)hsin3x3sin3x?3lim?lim求x?0sin2xx?02sin2x22xx2?1x?1lim?lim(x?1)?2x?1sin(x?1)x?1sin(x?1)求求求求求 tan3xsin3xlim?lim3cos3x?3x?0x?0x3x?x2?1(?x2?1)(?x2?1)lim?limx?0x?0si
5、nx(?x2?1)sinxx?lim?lim?022x?0x?0(?x?1)sinx?x?1sinxx?1xx?3?4x?4xlim()?lim()?lim(1?)x?x?3x?x?x?3x?3x?3(1?x2)?1x?4?4?4(1?)2x?6x?8(x?2)(x?4)2?e?4limlim? x?4x2?5x?4x?x?4(x?1)(x?4)33 (1?) 设函数 x?3?(x?2)2,x?1?f(x)?x,?1?x?1讨论f(x)的连续性,并写出其连续区间?x?1,x?1?x?1 解: x?1lim?f(x)?(1?2)2?1?lim?f(x)?1limf(x)?1?f(1)x?1lim
6、f(x)?1?limf(x)?1?1?0x?1?x?1?函数在x=1处连续x?1limf(x)不存在,函数在x=-1处不连续 高等数学基础第二次作业第3章 导数与微分(一)单项选择题f(x)f(x)存在,则lim?( B ) x?0x?0xxA. f(0) B. f?(0)C. f?(x) D. 0f(x0?2h)?f(x0) 设f(x)在x0可导,则lim?(D) h?02hA. ?2f?(x0)B. f?(x0)C. 2f?(x0) D. ?f?(x0)设f(0)?0且极限limf(1?x)?f(1)?(A) ?x?0?xA. e B. 2e11 C. eD. e 24设f(x)?x(x?
7、1)(x?2)?(x?99),则f?(0)?(D)设f(x)?e,则limxA. 99 B. ?99C. 99!D. ?99!下列结论中正确的是( C )A. 若f(x)在点x0有极限,则在点x0可导B. 若f(x)在点x0连续,则在点x0可导C. 若f(x)在点x0可导,则在点x0有极限D. 若f(x)在点x0有极限,则在点x0连续(二)填空题1?2?xsin,x?0 设函数f(x)?,则f?(0)? x?x?0?0,df(lnx)x2xx?设f(e)?e?5e,则dxx?1在(1,2)处的切线斜率是 曲线f(x)?sinx在(,1)处的切线方程是 42x2x 设y?x,则y?曲线f(x)?
8、设y?xlnx,则y?(三)计算题求下列函数的导数y?: y?(xx?3)ex y=(x3/2+3)ex,y=3/2x1/2ex+(x3/2+3)ex=(3/2x1/2+x3/2+3)exy?cotx?x2lnxy=-csc2x + 2xlnx +x x2y?y=(2xlnx-x)/ln2x lnxcosx?2xx32x6 y? y=(-sinx+2ln2)x-3x(cosx+2)/xx3y?lnx?x= sinx2y?x4?sinxlnxy=4x3-cosxlnx-sinx/x 1(?2x)sinx?(lnx?x2)cosxsin2xsinx?x2x2x2xy? y=(cosx+2x)3-(
9、sinx+x)3ln3/3 3x=cosx+2x-(sinx+x2)ln3/3xy?extanx?lnx y=extanx+exsec2x+1/x = ex(tanx+sec2x)+1/x 求下列函数的导数y?: y?e?xy?lncosx32y?xxx y=x7/8 y=(7/8)x -1/8 y?x?xy?cos2exy?cosexy?sinnxcosnx y=nsinn-1xcosxcosnx - nsinnxsin nx y?5sinxy?esinxy?xx?exy?xe?ee在下列方程中,y?y(x)是由方程确定的函数,求y?: ycosx?e2y方程对x求导:ycosx-ysinx
10、=2 ye2y 22222xxy=ysinx / (cosx-2e2y)y?cosylnx 方程对x求导:y = y (-siny)lnx +(1/x)cosyy=(1/x)cosy / (1+sinylnx) x22xsiny? 方程对x求导:2siny + y2xcosy=(2xy-x2 y)/y2 yy=2(xy y2siny) /(x2+2xy2cosy)y?x?lny 方程对x求导:y=1+ y/y, y=y /(y-1) lnx?ey?y2方程对x求导:1/x+ yey=2y y, y=1/x(2y-ey)y2?1?exsiny 方程对x求导:2y y=exsiny + y exc
11、osyy= exsiny/(2y- excosy)ey?ex?y3方程对x求导:yey =ex -3y2 y, y=ex/ey+3y2 y?5x?2y方程对x求导:y=5xln5 + y2yln2, y=5xln5 /(1-2yln2) 求下列函数的微分dy:y?cotx?cscx lnx sinx1?xy?arcsin 1?x1?xy? 1?xy?sin2ex y?y?tanex求下列函数的二阶导数:y?xlnxy?xsinxy?arctanxy?3x(四)证明题设f(x)是可导的奇函数,试证f?(x)是偶函数证明:由 f(x)= - f(-x) 求导f(x)= - f(-x)(-x) f(
12、x)= f(-x), f(x)是偶函数23篇二:高等数学基础形成性考核册答案篇三:2014年秋电大高等数学基础形成性考核册答案高等数学基础作业1第1章 函数第2章 极限与连续(一) 单项选择题下列各函数对中,(C )中的两个函数相等A. f(x)?(x)2,g(x)?x B. f(x)?x2,g(x)?xx2?13 C. f(x)?lnx,g(x)?3lnxD. f(x)?x?1,g(x)? x?1设函数f(x)的定义域为(?,?),则函数f(x)?f(?x)的图形关于(C)对称A. 坐标原点 B. x轴C. y轴D. y?x下列函数中为奇函数是(B)A. y?ln(1?x2)B. y?xco
13、sxax?a?x1?x)C. y?D. y?ln(2下列函数中为基本初等函数是(C)A. y?x?1 B. y?xC. y?x2?1,x?0 D. y? 1,x?0?下列极限存计算不正确的是(D)x2?1B. limln(1?x)?0A. lim2x?0x?x?2sinx1?0 D. limxsin?0C. limx?x?xx当x?0时,变量(C)是无穷小量sinx1 A.B. xx1 C. xsin D. ln(x?2) x若函数f(x)在点x0满足(A),则f(x)在点x0连续。A. limf(x)?f(x0)B. f(x)在点x0的某个邻域内有定义 x?x0f(x)?f(x0)D. li
14、mf(x)?limf(x)C. lim?x?x0x?x0x?x0(二)填空题 x2?9函数f(x)?ln(1?x)的定义域是?x|x?3?x?322已知函数f(x?1)?x?x,则f(x)? 1x)? lim(1?x?2x11x12x?1lim(1?)?lim(1?)2?e2 x?x?2x2x1?x?若函数f(x)?(1?x),x?0,在x?0处连续,则k? e?x?0?x?k,?x?1,x?0函数y?的间断点是x?0 sinx,x?0?若limf(x)?A,则当x?x0时,f(x)?A称为x?x0时的无穷小量 x?x0(二) 计算题设函数?ex,x?0f(x)? ?x,x?0求:f(?2),
15、f(0),f(1)解:f?2?2,f?0?0,f?1?e?e 12x?1的定义域 x?2x?1?x?0?2x?11?解:y?lg有意义,要求?解得?x?或x?0 x2?x?0?x?0?1?则定义域为?x|x?0或x? 2?在半径为R的半圆内内接一梯形,梯形的一个底边与半圆的直径重合,另一底边的两个端求函数y?lg点在半圆上,试将梯形的面积表示成其高的函数解:AO hBC设梯形ABCD即为题中要求的梯形,设高为h,即OE=h,下底CD2R直角三角形AOE中,利用勾股定理得AE?则上底2AE?h2R?hR? 2sin3x求lim x?0sin2x故S?sin3xsin3x?3xsin3x3133解
16、:lim?lim?lim? x?0sin2xx?0x?02122?2x2x2xx2?1求lim x?1sin(x?1)x2?1(x?1)(x?1)x?1?1?1?lim?lim?2 解:limx?1sin(x?1)x?1sin(x?1)x?11x?1tan3x求lim x?0xtan3xsin3x1sin3x11?lim?lim?3?1?3?3解:limx?0x?0xxcos3xx?03xcos3x1?x2?1求lim x?012?解:limx?0x?0x?0sinx?limx?0 x1)x?0?0 1?1?1求lim(x?x?1x) x?3111(1?)x(1?)?x?1x?1xe?1x?4
17、解:lim( )?lim()?lim?lim?ex3x?x?3x?x?xx?e11?(1?)(1?)33xx3x2?6x?8求lim2 x?4x?5x?4x2?6x?8?x?4?x?2?limx?2?4?2?2 解:lim2?limx?4x?5x?4x?4x?4x?1x?4x?14?131?设函数?(x?2)2,x?1?f(x)?x,?1?x?1?x?1,x?1?讨论f(x)的连续性,并写出其连续区间解:分别对分段点x?1,x?1处讨论连续性(1)x?1?x?1?limf?x?limx?1x?1?x?1?limf?x?lim?x?1?1?1?0所以limf?x?limf?x?,即f?x?在x?
18、1处不连续 x?1?x?1?(2)x?1?x?1?limf?x?lim?x?2?1?2?1x?1?x?1?22limf?x?limx?1f?1?1所以limf?x?limf?x?f?1?即f?x?在x?1处连续 x?1?x?1?由(1)(2)得f?x?在除点x?1外均连续故f?x?的连续区间为?,?1?第3章 导数与微分(一)单项选择题 ?1,? 高等数学基础第二次作业f(x)f(x)?(C ) 存在,则limx?0x?0xxA. f(0) B. f?(0)C. f?(x) D. 0cvxf(x0?2h)?f(x0)?(D )设f(x)在x0可导,则limh?02hA. ?2f?(x0)B.
19、f?(x0)C. 2f?(x0) D. ?f?(x0)设f(0)?0且极限limf(1?x)?f(1)?(A ) ?x?0?xA. e B. 2e11 C. eD. e 24设f(x)?x(x?1)(x?2)?(x?99),则f?(0)?(D )设f(x)?ex,则limA. 99 B. ?99C. 99!D. ?99!下列结论中正确的是( C )A. 若f(x)在点x0有极限,则在点x0可导B. 若f(x)在点x0连续,则在点x0可导C. 若f(x)在点x0可导,则在点x0有极限D. 若f(x)在点x0有极限,则在点x0连续(二)填空题1?2?xsin,x?0 设函数f(x)?,则f?(0)
20、? x?x?0?0,df(lnx)2lnx5 ?xxdx1 曲线f(x)?x?1在(1,2)处的切线斜率是k? 222? 曲线f(x)?sinx在(,1)处的切线方程是y?x?(1?) 4224设y?x2x,则y?2x2x(1?lnx)1 设y?xlnx,则y? x 设f(ex)?e2x?5ex,则(三)计算题求下列函数的导数y?: 3xy?(xx?3)e y?(x?3)e?x2e 2y?cotx?x2lnx y?csc2x?x?2xlnx xx3212xlnx?xx2y?y? 2lnxlnxcosx?2xx(?sinx?2xln2)?3(coxs?2x)y? y? 3xx41sinx(?2x)?(lnx?x2)cosx2lnx?xy?y? 2sinxsinxsinx3?cosxlnx y?x4?sinxlnxy?4x?xsinx?x23x(cosx?2x)?(sinx?x2)3xln3y? y? 32x3xex1xxx?y?etanx?lnx y?etan 2cosxx求下列函数的导数y?: y?e1?x2?xy?lncosx3 y?e?x2x2?sinx3223y?3x?3xtanx 3cosxy?78xxx ?17y?xy?x8 8y?x?x1?2?111y?(x?x2)3(1?x2) 322xy?cose
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