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高等数学基础归类复习
一、单项选择题
1-1下列各函数对中，（ C ）中的两个函数相等．
=x x2?13 C.f(x)=lnx，g(x)=3lnx D. f(x)=x+1，g(x)=
x?11-⒉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
设函数f(x)的定义域为(??,+?)，则函数f(x)?f(?x)的图形关于（D ）对称．
A. y=x B. x轴 C. y轴 D. 坐标原点
e?x?ex.函数y=的图形关于（ A ）对称．
2(A) 坐标原点 (B) x轴 (C) y轴 (D) y=x
A.
1-⒊下列函数中为奇函数是（ B ）． A.
f(x)=(x)2，g(x)=x B. f(x)=x2，g(x)y=ln(1+x) B. y=xcosx C.
2ax+a?xy=2 D.
y=ln(1+x)
下列函数中为奇函数是（A ）． A.
y=x3?x B. y=ex+e?x C. y=ln(x+1) D. y=xsinx
A
下列函数中为偶函数的是（ D ）．
y=(1+x)sinx B y=x2x C y=xcosx D y=ln(1+x2)
2-1 下列极限存计算不正确的是（ D ）．
x2=1 B. limln(1+x)=0 A. lim2x→?x+2x→0sinx1 C. lim=0 D. limxsin=0
x→?x→?xx2-2当x→0时，变量（ C ）是无穷小量．
sinx11A. B. C. xsin D. ln(x+2)
xxx1sinxxx当x→0时，变量（ C ）是无穷小量．A B C e?1 D 2
xxxsinx1x.当x→0时，变量（D ）是无穷小量．A B C 2 D ln(x+1)
xx下列变量中，是无穷小量的为（ B ）
11x?2 Asin(x→0) B ln(x+1)(x→0) Cex(x→?) D.2(x→2)
xx?4f(1?2h)?f(1)3-1设f(x)在点x=1处可导，则lim=（ D ）．
h→0h精品 1
设
学 海 无 涯
A. f?(1) B. ?f?(1) C. 2f?(1) D. ?2f?(1)
f(x0?2h)?f(x0)=（ D ）． f(x)在x0可导，则limh→0hA f?(x0) B 2f?(x0) C ?f?(x0) D ?2f?(x0)
设
f(x)在x0可导，则limA.
f(x0?2h)?f(x0)=（ D ）．
h→02h?2f?(x0) B. f?(x0) C. 2f?(x0) D. ?f?(x0)
?x→0设
f(x)=ex，则limf(1+?x)?f(1)11=（ A ） A e B. 2e C. e D. e
?x241dx=dx D.ln3-2. 下列等式不成立的是（D ）．
1xdx=d()
x2x11dx下列等式中正确的是（B ）．A.d( B. )=arctanxdxd()=?22x1+xxxx C.d(2ln2)=2dx D.d(tanx)=cotxdx
24-1函数f(x)=x+4x?1的单调增加区间是（ D ）．
A. (??,2) B. (?1,1) C. (2,+?) D. (?2,+?)
A.exdx=dex B ?sinxdx=d(cosx) C.
函数.函数
y=x2+4x?5在区间(?6,6)内满足（A ）．
A. 先单调下降再单调上升 B. 单调下降 C. 先单调上升再单调下降 D. 单调上升
y=x2?x?6在区间（－5，5）内满足（ A ）
A 先单调下降再单调上升 B 单调下降 C先单调上升再单调下降 D 单调上升
. 函数
y=x2?2x+6在区间(2,5)内满足（D ）．
A. 先单调下降再单调上升 B. 单调下降 C. 先单调上升再单调下降 D. 单调上升
5-1若
f(x)的一个原函数是
1，则f?(x)=（D ）． A. lnxx B.
?1x2 C.
12 D. 3xx
.若F(x)是 AC5-2若
f(x) 的一个原函数，则下列等式成立的是（ A ）。
?xaf(x)dx=F(x)?F(a) B
?babF(x)dx=f(b)?f(a)
f?(x)=F(x) D?f?(x)dx=F(b)?F(a)
af(x)=cosx，则?f?(x)dx=（ B ）．
A. sinx+c B. cosx+c C. ?sinx+c D. ?cosx+c
下列等式成立的是（D ）．
A. C.
?f?(x)dx=f(x) B. ?df(x)=f(x)
d?f(x)dx=f(x) D.
df(x)dx=f(x) dx?d11323233f(x)xf(x)（ B ）． A. B. C. D. xf(x)dx=f(x)f(x) ?dx33d11222xf(x)xf(x)dx （ D ） A B C D xf(x)dx=f(x)dxf(x)dx?221f(x)dx=（ B ）． ⒌-3若?f(x)dx=F(x)+c，则?x1F(x)+c A. F(x)+c B. 2F(x)+c C. F(2x)+c D.
x精品
2
学 海 无 涯
补充：
?x?x?xef(e)dx= ?F(e)+c, 无穷积分收敛的是 ??+?11dx 2x 函数
二、填空题
f(x)=10x+10?x的图形关于 y 轴 对称。
x2?9+ln(1+x)的定义域是 （3，+∞） ．
x?3⒈函数f(x)=函数
x+4?x的定义域是 （2，3） ∪ （3，4 ]
ln(x?2)1函数f(x)=ln(x+5)?的定义域是 （－5，2）
2?x?x2+1,x?0若函数f(x)=?，则f(0)= 1 ．
x2,x?0?1?x?2若函数f(x)=?(1+x),x?0，在x=0处连续，则k= e
?x?0?x+k,?sin2x?x?0.函数f(x)=?x在x=0处连续，则k= 2
?x=0?k?x+1,x?0函数y=?的间断点是 x=0 ．
?sinx,x?0x2?2x?3函数y=的间断点是 x=3 。
x?31函数y=的间断点是 x=0
1?ex3-⒈曲线f(x)=x+1在(1,2)处的切线斜率是 1/2 ．
y=曲线曲线.曲线
．
f(x)=x+2在(2,2)处的切线斜率是 1/4 ．
f(x)=ex+1在（0，2）处的切线斜率是 1 ．
f(x)=x3+1在(1,2)处的切线斜率是 3 ．
π3-2 曲线f(x)=sinx在(,1)处的切线方程是 y = 1 ．切线斜率是 0 2曲线y = sinx 在点 (0,0)处的切线方程为 y = x 切线斜率是 1
4.函数y=ln(1+x)的单调减少区间是 （－∞，0 ） ．
2f(x)=ex的单调增加区间是 （0，+∞） ．
2.函数y=(x+1)+1的单调减少区间是 （－∞，－1 ） ．
2.函数f(x)=x+1的单调增加区间是 （0，+∞） ．
函数 函数5-1d2y=e?x22的单调减少区间是 （0，+∞） ．
?xe?dx=
e?xdx
2 ． .
d22 ． sinxdx=sinx?dx?(tanx)?dx= tan x +C ．
若?f(x)dx=sin3x+c，则f?(x)= －9 sin 3x ．
5-2
1(sinx+)dx= 3 ． ??3235x3dedx= 0 ． ln(x+1)dx= 0 ??1x2+1?1dx1精品 3
电大高等数学基础考试答案完整版(整理)(7月20日).pdf
