天一专升本绝密试卷第4套
高等数学试卷 第1页 （共6页）
高等数学试卷
说明：考试时间120分钟，试卷共150分。
一、单项选择题（每小题2分，共50分。在每个小题的备选答案中选出一个 正确答案，并将其代码写在题干后的括号内。）
1．设133ln
)(+-+=x
x
x f ，则??
?
??+x f x f 3)(的定义域为 ( ) (A) ()1,3- (B) ()3,1
(C) ()3,3- (D) ()() 3,11,3--
2．下列函数中，图形关于直线x y =对称的是 ( )
(A) x x y c o s = (B) 2
22x
x y -+=
(C) 2
21-+=x x
y (D) 12++=x x y
3．当0→x 时，下列函数是其它三个的高阶无穷小的是 ( )
(A) 2
x x + (B) x cos 1-
(C)1-x
a (D) ()
x -1ln
4．=?
?
?
??+++∞→1
1232lim x x x x ( )
(A) 2
1
-e
(B) 2
1e
(C) e (D) 2
3e
5．()x f 在0x 点连续，()x g 在0x 点不连续，则()()x g x f +在0x 点 ( ) (A) 一定连续 (B) 一定不连续
(C) 可能连续，也可能不连续 (D) 无法判断 6．假定()0x f '存在，则 ()()
=--+→h
nh x f mh x f h 000lim
( )
(A) ()0x f m ' (B) ()0x f n '
(C) ()()0x f n m '+ (D) ()()0x f n m '-
高等数学试卷 第2页 （共6页）
7.由方程()11ln
sin =+-y x xy ，所确定的隐函数()y x x =的导数dy dx
为 ( ) (A) ()()xy y x y
xy x cos 111cos -++ (B) ()
()xy x y
xy y x cos 1cos 11
+-+
(C) ()xy y
x cos 1
11
++ (D) ()xy x y cos 1
1
1-+
8．x
x
y -+=
11，则 ()=n y ( ) (A) ()
n
x n -?11
!
2 (B) ()
1
11
!
+-n x n
(C) ()()
1
11
!
21+-?-n n
x n (D) ()
1
11
!
2+-?n x n
9．下列函数在给定的区间满足拉格朗日中值定理条件的是 ( )
(A) ()[]1,1,1
sin
-=x
x f (B) ()[]1,1,132--=x x f (C) ()()[]1,1,2ln -+=x x f (D) ()[]??
?-<≥-=1,1,0
10
1x x x f
10．已知函数()x f 在区间()δδ+-1,1内具有二阶导数，()x f '严格单调减少，且()()111='=f f ， 则 ( )
(A) 在()1,1δ-和()δ+1,1内均有()x x f < (B) 在()1,1δ-和()δ+1,1内均有()x x f >
(C) 在()1,1δ-内()x x f <，在()δ+1,1内()x x f > (D) 在()1,1δ-内()x x f >，在()δ+1,1内()x x f <
11．曲线1
-=x x e e y ( )
(A) 有一条水平渐近线，一条垂直渐近线 (B)有两条水平渐近线，一条垂直渐近线
(C) 有一条水平渐近线，两条垂直渐近线
(D) 只有垂直渐近线
12．设参数方程为???-=+'=t
t y e t x 3123
，则 ==1
22x dx y
d ( )
高等数学试卷 第3页 （共6页）
(A) 43 (B) 23 (C) 283e (D) e 8
3
13．设?+=C x xdx k 2cos ln 4
1
2tan ，则k= ( )
(A) 1- (B) 2
1
-
(C ) 31- (D) 4
1
-
14．()x f 有一个原函数x
x
sin ，则 ()?='dx x f ( )
(A) C x +-c o s (B ) C x
x
x x +-2
sin cos (C) C x
x
x +-
sin sin (D) 无法计算 15．
=+?
∞
1
2)
1(x x dx
( )
(A) 2ln (B) 2ln - (C ) 2ln 2
1
(D) 发散 16．
p dx x f dx x f a
a
a
+=??
-0
)()(，则p= ( )
(A) ?
a
dx x f 0)( (B) ?
-0
)(a
dx x f
(C )
?
-a
dx x f 0
)( (D)
?
--0)(a
dx x f
17．设x e f x +='1)(，则f(x)= ( )
(A) C x +ln (B) C x +-ln (C ) C x x +ln (D)
C x
x
+ln 18．在下列积分中，其值为0的是 ( )
(A) dx x ?-
π
π
2sin (B) dx x ?-1
1
2cos
(C )
dx x ?-π
π
2cos (D)
dx x ?
-1
1
2cos
19．设)(x f '为连续函数，则下列命题正确的是 ( ) (A)
)()(x f dx x f b
a
='? (B)
)()(x f dx x f dx d b
a =? (C ) )()(x f dx x f ='? (D)
)()(x f dt t f dx d x
a
=?
高等数学试卷 第4页 （共6页）
20．直线??
?--==-z
y y
x 223与平面01=+--z y x 的关系是 ( )
(A) 垂直 (B) 相交但不垂直 (C ) 直线在平面上 (D) 平行
21．当0→x 时，2x 是x
x e e -tan 的 （ ）
( A) 高阶无穷小 ( B) 低阶无穷小
(C ) 等价无穷小 (D) 同阶无穷小但非等价无穷小 22．对于函数x
y 111-=
，下列结论正确的是 ( )
(A) x=0是第一类间断点，x=1是第二类间断点 (B) x=0是第二类间断点，x=1是第一类间断点
(C ) x=0是第一类间断点，x=1是第一类间断点 (D) x=0是第二类间断点，x=1是第二类间断点
23．设曲线12++=ax x y 在点x=1处的切线斜率为1-，则常数a 为 ( )
( A) 3- ( B) 2- (C ) 1- (D) 1
24．设f(x)在[a,b]上连续，在（a,b ）内可导，且f(a)=f(b),则曲线y=f(x)在（a,b ）内平行于x 轴的切
线 ( ) ( A) 仅有一条 ( B) 至少有一条
(C ) 有两条 (D) 不存在 25．设
?
=a
dx x 0
29，则常数 a = ( )
( A) 3 ( B) 2
9 (C ) 2 (D) 3-
二、填空题（每小题2分，共30分）
1． ?????>+≤=0
0)(2
2x x
x x x
x f ，则=-)(x f ______________
2． 设??
?>+≤-=02
2)(x x x x
x g ；???≥-<=0
)(2x x
x x x f ，则g[f （x ）]=______________ 3． 设)1(1
)1(
-≠+=-x x x
x x f ，则=')1(f _________________________\
高等数学试卷 第5页 （共6页）
4． 函数x x f arcsin ln )(=的连续区间是_______________
5． 设
1)1()(--=x x x f ，则=')1(f _______________
6． 由方程y
x
x y =所确定的隐函数)(x y y =的导数dx
dy
=________________________
7． 若
)(x f 是可导函数，)(cos )(sin 22x f x f y +=，则y '=___________________
8． 曲线3x y =与直线q px y -=（其中p>0）相切，则p=____________________
9．设)(x f y =是方程042=+'-''y y y 的一个解，若,0)(0>x f 且,0)(0='x f 则函数在0x 有极值____________________
10．满足0)()(=-'+'x f x x f 的函数f （x ）是______________________________ 11．定积分
=+?-
dx x x π
π
)sin (2______________
12．已知a,b,c 为非零向量，且两两不平行，但a+b 与c 平行，b+c 与a 平行，则a+b+c=_____________ 13．==)1,1,1(,du y
x
z
u ____________ 14．交换二次积分顺序：
=??
dy y x f dx x
1
),( ________________
15．微分方程096=+'-''y y y 的通解为 ________________
三、计算题（每小题5分，共40分）
1．求2
111
sin lim
x
x e x x ----→
2．设3
412++=x x y ，求.)
(n y
3．计算?++dx x x )1ln(2
4．计算dx x x ?
-10
22。
5．设)(),(u F x y xF xy z +=为可导函数，
证明：xy z y
z y x z x +=??+??. 6．求
δd y x
D
??+)(22
，其中D 是由,,x y a x y =+=及y=3a (a >0)为边的平行四边形。
高等数学试卷 第6页 （共6页）
7．将函数2
23
)(x x x f -+=
展成x 的幂级数，并指明收敛区间。
8．求解微分方程1)(,0)ln (ln ==-+e y dx x y xdy x 。
四、应用题（每小题7分，共21分）
1． 向宽为a 米的河修建一宽为b 米的运河，二者直角相交，问能驶进运河的船，其最大长度为多
少？
2．求由曲线32)1(-=x y 和直线2=x 所围成的图形绕ox 轴旋转所得旋转体体积。 3．求微分方程02
3=+'+y e y x
y 满足条件1,0==y x 的特解。
五、证明题（9分）
试证：当x>0时，有.2
1arctan π>+x x 。
天一专升本高数知识点
天一专升本高数知识点 Company number：【WTUT-WT88Y-W8BBGB-BWYTT-19998】
第一讲 函数、极限、连续 1、基本初等函数的定义域、值域、图像，尤其是图像包含了函数的所有信息。 2、函数的性质，奇偶性、有界性 奇函数：)()(x f x f -=-，图像关于原点对称。 偶函数：)()(x f x f =-，图像关于y 轴对称 3、无穷小量、无穷大量、阶的比较 设βα，是自变量同一变化过程中的两个无穷小量，则 （1）若0=β α lim ，则α是比β高阶的无穷小量。 （2）若c β α =lim （不为0），则α与β是同阶无穷小量 特别地，若1=β α lim ，则α与β是等价无穷小量 （3）若∞=β α lim ，则α与β是低阶无穷小量 记忆方法：看谁趋向于0的速度快，谁就趋向于0的本领高。 4、两个重要极限 （1）100==→→x x x x x x sin lim sin lim 使用方法：拼凑[][ ][][][][] 000 ==→→sin lim sin lim ，一定保证拼凑sin 后面和分母保持一致 （2）e x x x x x x =+=??? ? ?+→∞→1 0111)(lim lim 使用方法1后面一定是一个无穷小量并且和指数互为倒数，不满足条件得拼凑。
5、()() ? ?>∞<==∞→m n m n m n b a X Q x P m n x ,,,lim 00 ()x P n 的最高次幂是n,()x Q m 的最高次幂是m.,只比较最高次幂，谁的次幂高，谁的头大，趋向于无穷大的速度快。m n =,以相同的比例趋向于无穷大；m n <，分母以更快的速度趋向于无穷大； m n >，分子以更快的速度趋向于无穷大。 7、左右极限 左极限：A x f x x =-→)(lim 0 右极限：A x f x x =+→)(lim 0 注：此条件主要应用在分段函数分段点处的极限求解。 8、连续、间断 连续的定义： []0)()(lim lim 000 =-?+=?→?→?x f x x f y x x 或)()(lim 00 x f x f x x =→ 间断：使得连续定义)()(lim 00 x f x f x x =→无法成立的三种情况 记忆方法：1、右边不存在 2、左边不存在 3、左右都存在，但不相等 9、间断点类型 （1）、第二类间断点：)(lim 0 x f x x -→、)(lim 0 x f x x +→至少有一个不存在 （2）、第一类间断点：)(lim 0 x f x x -→、)(lim 0 x f x x +→都存在 注：在应用时，先判断是不是“第二类间断点”，左右只要有一个不存在，就是“第二类”然后再判断 是不是第一类间断点；左右相等是“可去”，左右不等是“跳跃” 10、闭区间上连续函数的性质 （1） 最值定理：如果)(x f 在[]b a ,上连续，则)(x f 在[]b a ,上必有最大值最小值。
专升本高数真题及答案
2005年河南省普通高等学校 选拔优秀专科生进入本科阶段学习考试 高等数学 试卷 一、单项选择题（每小题2分，共计60分） 在每小题的四个备选答案中选出一个正确答案，并将其代码写在题 干后面的括号内。不选、错选或多选者，该题无分. 1. 函 数 x x y --= 5)1ln(的定义域为为 （ ） A.1>x 5
解： ?-x e x ~12~12 x e x -,应选B. 4.=?? ? ??++∞ →1 21lim n n n （ ） A. e B.2e C.3e D.4e 解：2)1(2lim 2 )1(221 21lim 21lim 21lim e n n n n n n n n n n n n n n =? ?? ????? ??? ??+=?? ? ??+=?? ? ? ? + +∞→+?∞ →+∞ →∞→,应选B. 5.设 ?? ? ??=≠--=0,0,11)(x a x x x x f 在0=x 处连续，则 常数=a （ ） A. 1 B.-1 C.21 D.2 1 - 解：2 1 )11(1lim )11(lim 11lim )(lim 0000 =-+=-+=--=→→→→x x x x x x x f x x x x ,应选C. 6.设函数)(x f 在点1=x 处可导,且2 1 )1()21(lim 0 =--→h f h f h ,则=')1(f （ ） A. 1 B.21- C.41 D.4 1 - 解：4 1 )1(21)1(22)1()21(lim 2)1()21(lim 020-='?='-=----=--→-→f f h f h f h f h f h h , 应选D. 7.由方程y x e xy +=确定的隐函数)(y x 的导数dy dx 为 （ ） A. )1()1(x y y x -- B.)1()1(y x x y -- C.)1()1(-+y x x y D.) 1() 1(-+x y y x 解：对方程y x e xy +=两边微分得)(dy dx e ydx xdy y x +=++, 即dy x e dx e y y x y x )()(-=-++, dy x xy dx xy y )()(-=-,
专升本英语阅读理解50篇
专升本英语阅读理解50 篇 (1) One sho u ld be moderate（适度）in a ll things. Moderation i s a l ways the safes t way to do t h ing s and a v irtu e（品质）we shou ld have. Let's take th e stodcnt Ii fe for exam pl e. The re arc some students who s tu dy too hard a nd play 100 little, while there are o th ers who play too mu c h and study too linle. On o n e hand, it is harm fu l 10 his heallh i f h c ha s too few exercises, and on the o th e r hand, i t is harmful 10 h is mind if h c pl ays t oo mu c h. In th e matter of eating, one a l so shou l d be m odera t e. Do not eat 100 much or 100 li ule. Too much eat in g wi ll m ake you s ick, whi l e 100 litt le eating will make yo u weak T h e man of progrcss i s h e who neithcr has I OO h ig,h an opin i on of h imse lf nor Ihin ks lOO poorly of h imse lf. l f a man thinks 100 hig h ly of h imse l f, he is sure 10 become very pro ud, but ifhe has 100 poor an o pini on of h i m self, h e w ill ha ve no courage 10 make an adva n ce. Bo 由lh c cond 山ons above wi ll make you l ose your advancing a im. A broad m i nded man i s he w h o a l ways moves with in the o rbit （轨道）of rca onab l cness. W h c1hcr in any aetivilies in life, moderation i s one of the be t ways 10enjoy re a l happin css. I . ''Someone c modcra1e" mea n s A.he wa l ks neither 100 fast nor 100 s l owly B.h e hasgood characters and good ways to do things C. h e i s not on l y safe bu1 a l so successful D. he i s e i1h crt a ll o r shor l 2.T h e ,vriter s u gge 1s that a st u dcn l shou l d A, have much more time to st ud y 1han10 play B.spend m ost of 1h c time playing difleren1 games C.on l y study hard w i t h o ut any 1irne to play D.correct l y arrange （安排）h i s time for study and play 3. Modcra1c eating m eans A.eating as much food as o n e ca n if 1he food i s 1a t y B.eating food ri ch of fa1 C.eati n g a proper amounl of food D.eating either too much or 100 l i1t l e 4 , If one want to be br oad-minded. he must A.believe in himself B.be full of co u r age C.enjoy rea l happine s D, do every1h ing that i s reasonable 答案：B D C D (2) Daniel Boone was born in the U n i ted States in 1734. He didn't go to schoo l a nd cou l dn't r ead, a lth ough h e l earned a ll about th e fo r csl , streams and hunting. He could move sile nt ly lik e an Indian l eaving no marks. He l oved to li ve alone in th e woods where nothing frightened him When he grew up, he married an d tri ed t o 沁ide down o n a farm. A year la t er, however, h e wasn't sa ti sfie d a nd decided t o go i nt o the unknown western land s, crossing the Appalachian Mou nt ai n s. Whe n he returned a 仆er l\vo years, hebecame famous for h is lo n g journey. He brought va lu ab l e an im a l sk in s and t o ld stories about the Indians. After thi s, he cho沁10 keep travelling to unknown places. Once he lost t o the Indians in batt le and was taken away. T h e Indian. li ked him and bec"1me his frie n岱 Daniel Boone died a t the age of86.He i s remembered as a n ex p lo r c（-r探险者）a nd a p i o n eer who lived an exciting li fe in the early years of American nation I . Daniel Boone's ea-rly li fe was mainly s p en t i n A. l earn ing about nature 8. hunting wi th his friends
专升本高等数学知识点汇总
------------------- 时需Sr彳-------- ---- --- -- 专升本高等数学知识点汇总 常用知识点： 一、常见函数的定义域总结如下： y kx b (1) 2 —般形式的定义域：x € R y ax bx c k (2)y 分式形式的定义域：x丰0 x (3)y 、、x根式的形式定义域：x > 0 (4)y log a x对数形式的定义域：X>0 二、函数的性质 1、函数的单调性 当洛X2时，恒有f(xj f(X2), f(x)在x1?X2所在的区间上是增加的。 当x1 x2时，恒有f (x1) f (x2) , f (x)在x1?x2所在的区间上是减少的。 2、函数的奇偶性 定义：设函数y f(x)的定义区间D关于坐标原点对称(即若x D，则有x D ) (1)偶函数f (x)——x D，恒有f ( x) f (x)。 ⑵奇函数f (x)——x D，恒有f( x) f (x)。 三、基本初等函数 1、常数函数：y c，定义域是(，)，图形是一条平行于x轴的直线。 2、幕函数：y x u, (u是常数)。它的定义域随着u的不同而不同。图形过原点。 3、指数函数
定义：y f（x）x a，I （a是常数且a 0，a 1）.图形过（0,1）点。 4 、 对数函数 定义：y f （x）lOg a X，（a是常数且a 0，a1）。图形过（1,0 )点。5 、 三角函数 (1)正弦函数：y sin x T 2 ，D(f)(,)，f (D) [ 1,1]。 ⑵余弦函数：y cosx. T 2 ，D(f)(,)，f (D) [ 1,1]。 ⑶正切函数：y tan x T，D(f) {x | x R,x (2k 1)-,k Z}，f(D)(,). ⑷余切函数：y cotx T，D(f) {x | x R,x k ,k Z}，f(D)(,). 5、反三角函数 （1）反正弦函数：y arcsinx，D( f) [ 1,1]，f (D)[,]。 2 2 （2）反余弦函 数： y arccosx，D(f) [ 1,1]，f(D) [0,]。 （3）反正切函数：y arctanx，D(f) ( , )，f (D)(-,- 2 2 （4）反余切函 数： y arccotx，D(f) ( , )，f(D) (0,)。 极限 一、求极限的方法 1代入法 代入法主要是利用了“初等函数在某点的极限，等于该点的函数值。”因此遇到大部分简单题目的时候，可以直接代入进行极限的求解。 2、传统求极限的方法 （1）利用极限的四则运算法则求极限。 （2）利用等价无穷小量代换求极限。 （3）利用两个重要极限求极限。 （4）利用罗比达法则就极限。
天一专升本高数知识点
第一讲 函数、极限、连续 1、基本初等函数的定义域、值域、图像，尤其是图像包含了函数的所有信息。 2、函数的性质，奇偶性、有界性 奇函数：)()(x f x f -=-，图像关于原点对称。 偶函数： )()(x f x f =-，图像关于y 轴对称 3、无穷小量、无穷大量、阶的比较 设βα，是自变量同一变化过程中的两个无穷小量，则 （1）若0=β α lim ，则α是比β高阶的无穷小量。 （2）若c β α =lim （不为0），则α与β是同阶无穷小量 特别地，若1=β α lim ，则α与β是等价无穷小量 （3）若∞=β α lim ，则α与β是低阶无穷小量 记忆方法：看谁趋向于0的速度快，谁就趋向于0的本领高。 4、两个重要极限 （1）100==→→x x x x x x sin lim sin lim 使用方法：拼凑[][ ][][][][] 000 ==→→sin lim sin lim ，一定保证拼凑sin 后面和分母保持一致 （2）e x x x x x x =+=??? ? ?+→∞→1 0111)(lim lim [][][]e =+→1 1)(lim 使用方法1后面一定是一个无穷小量并且和指数互为倒数，不满足条件得拼凑。
5、()() ? ?>∞<==∞→m n m n m n b a X Q x P m n x ,,,lim 00 ()x P n 的最高次幂是n,()x Q m 的最高次幂是m.,只比较最高次幂，谁的次幂高，谁的头大，趋向于无穷大的速度 快。m n =,以相同的比例趋向于无穷大；m n <，分母以更快的速度趋向于无穷大；m n >，分子以更快的速度趋向于无穷大。 7、左右极限 左极限：A x f x x =- →)(lim 0 右极限：A x f x x =+ →)(lim 0 A x f x f A x f x x x x x x ===+ - →→→)(lim )(lim )(lim 000 充分必要条件是 注：此条件主要应用在分段函数分段点处的极限求解。 8、连续、间断 连续的定义： []0)()(lim lim 000 =-?+=?→?→?x f x x f y x x 或)()(lim 00 x f x f x x =→ 间断：使得连续定义)()(lim 00 x f x f x x =→无法成立的三种情况 ??? ? ???≠→→)()(lim )(lim )()(00 00 0x f x f x f x f x f x x x x 不存在无意义 不存在， 记忆方法：1、右边不存在 2、左边不存在 3、左右都存在，但不相等 9、间断点类型 （1）、第二类间断点：)(lim 0 x f x x - →、)(lim 0x f x x + →至少有一个不存在 （2）、第一类间断点：)(lim 0 x f x x - →、)(lim 0x f x x + →都存在
2015专升本阅读理解练习及答案详解
Reading Comprehension (January, 2015) Passage 1 Packaging is an important form of advertising. A package can sometimes motivate someone to buy a product. For example, a small child may ask for a breakfast food that comes in a box with a picture of a TV character. The child is more interested in the picture than in breakfast food. Pictures for children to color or to cut out, games printed on a package or small gifts inside a box also motivate many children to buy products, or to ask their parents to buy for them. Some packages suggest that a buyer will get something for nothing. Food products sold in reusable container are examples of this. Although a similar product in a plain container may cost less, people often prefer to buy the product in a reusable glass or dish, because they believe the container is free. However, the cost of the container is added to the cost of the product. The size of the package also motivates a buyer. Maybe the package has “Economy Size” or “Family Size” painted on it. This sugges ts that the large size has the most products for the least money. But that is not always true. To find out, a buyer has to know how the product is sold and the price of the basic unit. The information on the package should provide some answers. But the important thing for any buyer to remember is that a package is often an advertisement. The words and pictures do not tell the whole story. Only the product inside can do that. 1. As used in the passage, the word “motivate” most probably means______. A) making one deep in thought B) supplying a thought or feeling that makes one act C) providing a story that makes one move D) making one believe what he does is just right 2. A buyer will get something for nothing most probably means that ______. A) a buyer will get something useful free of charge B) a buyer will get what he pays for C) a buyer will gain more than he loses D) a buyer will not get what he wants 3. People are likely to buy the product sold in a glass or dish because ______. A) they believe the cost of the container is included in the cost of the product B) the container is too attractive C) they think they can get the container for free D) they have no other choice 4. Which of the following statements is NOT mentioned in the passage? ______. A) Package is often a successful advertisement B) Children are often encouraged to buy a product by its package with attractive pictures C) A buyer is also attracted by the size of the container D) On seeing a well-designed container, a buyer often neglects what is in it 5. What suggestion does the author give in the passage? ______. A) The quality of the container has nothing to do with the quality of the product B) Don’t buy the product w hich is sold in a glass or dish C) A buyer should get what he needs most D) The best choice for a buyer is to get a product in a plain package Passage 2 China is pushing forward a nationwide trial on fortified (强化的)food, in a bid to improve the health of its citizens. About 30,000 people from the country’s western region have used fortified flour for two years. Their diets had been improved. This experience will be promoted throughout the country and fortified oil and rice have also been introduced across the country. Fortified food refers to food with nutrients (营养) added, such as vitamins, calcium and iron. The nutrition program is expected to be included in the key projects for the country’s 11th Five-Year Plan (2006-2010). A series of rules and regulations, such as nutrition rules and production standards for fortified flour, will come into effect. The intake of some nutrients, such as fat, protein and calories is often excessive, but some other nutrients, such as vitamins, are lacking in some diets, according to some experts. At the moment there are three ways to improve public nutrition ---- a balanced diet, food fortification and nutritional supplements(补充). However, due to China’s massive population and its unbalanced economic development, food fortification is thought to be the best way of improving public nutrition in a short period of time. China started fortifying food in 2002, while developed countries such as the United States have more than 50 years of such experience. “Fortified foods do not sell well, as the public still knows little about it.” Some experts pointed out. 1. What is the purpose for China to push forward the plan on fortified food? . A) To improve the health of its citizens B) To advise its citizens to use fortified flour C) To introduce fortified oil and rice
专升本高等数学知识点汇总
专升本高等数学知识点汇总 常用知识点： 一、常见函数的定义域总结如下： （1） c bx ax y b kx y ++=+=2 一般形式的定义域：x ∈R （2）x k y = 分式形式的定义域：x ≠0 （3）x y = 根式的形式定义域：x ≥0 （4）x y a log = 对数形式的定义域：x ＞0 二、函数的性质 1、函数的单调性 当21x x <时，恒有)()(21x f x f <，)(x f 在21x x ，所在的区间上是增加的。 当21x x <时，恒有)()(21x f x f >，)(x f 在21x x ，所在的区间上是减少的。 2、 函数的奇偶性 定义：设函数)(x f y =的定义区间D 关于坐标原点对称（即若D x ∈，则有D x ∈-） (1) 偶函数)(x f ——D x ∈?，恒有)()(x f x f =-。 (2) 奇函数)(x f ——D x ∈?，恒有)()(x f x f -=-。 三、基本初等函数 1、常数函数：c y =，定义域是),(+∞-∞，图形是一条平行于x 轴的直线。 2、幂函数：u x y =， (u 是常数)。它的定义域随着u 的不同而不同。图形过原点。 3、指数函数
定义: x a x f y ==)(， (a 是常数且0>a ，1≠a ).图形过（0,1）点。 4、对数函数 定义: x x f y a log )(==， (a 是常数且0>a ，1≠a )。图形过（1,0）点。 5、三角函数 (1) 正弦函数: x y sin = π2=T ， ),()(+∞-∞=f D ， ]1,1[)(-=D f 。 (2) 余弦函数: x y cos =. π2=T ， ),()(+∞-∞=f D ， ]1,1[)(-=D f 。 (3) 正切函数: x y tan =. π=T ， },2 ) 12(,|{)(Z R ∈+≠∈=k k x x x f D π ， ),()(+∞-∞=D f . (4) 余切函数: x y cot =. π=T ， },,|{)(Z R ∈≠∈=k k x x x f D π， ),()(+∞-∞=D f . 5、反三角函数 (1) 反正弦函数: x y sin arc =，]1,1[)(-=f D ，]2 ,2[)(π π- =D f 。 (2) 反余弦函数: x y arccos =，]1,1[)(-=f D ，],0[)(π=D f 。 (3) 反正切函数: x y arctan =，),()(+∞-∞=f D ，)2 ,2()(π π- =D f 。 (4) 反余切函数: x y arccot =，),()(+∞-∞=f D ，),0()(π=D f 。 极限 一、求极限的方法 1、代入法 代入法主要是利用了“初等函数在某点的极限，等于该点的函数值。”因此遇到大部分简单题目的时候，可以直接代入进行极限的求解。 2、传统求极限的方法 （1）利用极限的四则运算法则求极限。 （2）利用等价无穷小量代换求极限。 （3）利用两个重要极限求极限。 （4）利用罗比达法则就极限。
2017年专升本高等数学真题试卷
高等数学 请考生按规定用笔将所有试题的答案涂、写在答题纸上。 选择题部分 注意事项: 1.答题前，考生务必将自己的姓名、准考证号用黑色字迹的签字笔或钢笔填写在答题纸规定 的位置上。 2.每小题选出答案后，用 2B 铅笔把答题纸上对应题目的答案标号涂黑，如需改动，用橡皮 擦干净后，再选涂其它答案标号。不能答在试题卷上。 一、选择题: 本大题共5小题,每小题4分,共 20分。在每小题给出 的四个选项中，只有一项是符合题目要求的。 1．已知函数1 x ()e f x =，则x=0是函数f(x)的（ ）． （A ）可去间断点 （B ）连续点 （C ）跳跃间断点 （D ）第二类间断点 2. 设函数f(x)在[a,b]上连续，则下列说法正确的是 （A ）b a ()()()f x dx f b a ζζ∈=-?必存在（a,b ）,使得 （B ）'()()f b a ζζ∈-必存在（a,b ）,使得f(b)-f(a)= （C ）()0f ζξ∈=必存在（a,b ）,使得 （D ）'()0f ζζ∈=必存在（a,b ）,使得 3 下列等式中，正确的是 （A ）'()()f x dx f x =? （B ）()()df x f x =?（C ）()()d f x dx f x dx =? （D ）()()d f x dx f x =? 4. 下列广义积分发散的是 （A ）+2011+dx x ∞ ? （B ）12 011dx x -? （C ）+0ln x dx x ∞? （D ）+0x e dx ∞-? 5． y -32sin ,x y y e x '''+=微分方程则其特解形式为 （A ）sin x ae x （B ）(cos sin )x xe a x b x +
[专升本类试卷]河北专接本英语(阅读理解)模拟试卷7.doc
[专升本类试卷]河北专接本英语（阅读理解）模拟试卷7 0 Long before recorded history, our ancestors were bathing for pleasure and health. The earliest records often mention the use of rivers for bathing. And the Hindus have believed for centuries that the Ganges River has the power to clean the soul, as well as the body. Several thousand years ago, the inhabitants of the island of Crete built baths with running water. The early Jews took ceremonial baths on certain occasions, making use of oils and ointments(油膏). The Jews also had a custom of bathing the feet of all strangers that came within their gates. This friendly custom is still practised in parts of Palestine. Swimming was popular among the Greeks of ancient time. By the third century before Christ, almost every Greek city of a certain size had at least one public bath. The wealthy classes had private baths and pools, some of which were beautifully decorated. Many of the public baths that the Romans built utilized natural mineral springs. Since most of these springs were naturally warm the Romans took advantage of this free hot water. By the time of the Roman Emperors, these baths were often housed in large, marble(大理石) buildings. The baths built by the Emperor Caracalla, in the center of Rome, covered about one square mile and could hold sixteen thousand people. 1 The earliest bathing place was probably_____. （A）the river （B）the Nile （C）the Ganges （D）the River Jordan 2 According to the passage, today, some parts of Palestine also have the custom of_____. （A）bathing in public baths （B）bathing for pleasure
天一专升本高数知识点
第一讲函数、极限、连续 1、 基本初等函数的定义域、值域、图像，尤其是图像包含了函数的所有信息。 2、 函数的性质，奇偶性、有界性 设 a, 3是自变量同一变化过程中的两 个无穷小量，则 a (1)若lim 一 = 0，则a 是比 3 a （2）若 lim — = C （不为 0）, 3 a (3)若 lim — = 3 记忆方法：看谁趋向于 4、两个重要极限 ，贝y a 与3是低阶无穷小 量 sinx X , =lim ----- =1 X T 。si nx 拼凑 lfm*] Tm 。*] =0，一定保证拼凑sin 后面和分母保持一致 ⑵ lim1」「lim （1+xle X X 丿 X T 。 1 时〔卩Le 使用方法1后面一定是一个无穷小量并且和指数互为倒数，不满足条件得拼凑。 奇函数: f(-x)=-f(x), 图像关于原点对称。 偶函数: f (-X)= f(x), 图像关于y 轴对称 3、无穷小量、 无穷大量、阶的比较 特别地，若 lim — =1，则 3 a 与3是等价无穷小量 (3高阶的无穷小量。 则 a 与3是同阶无穷小量 0的速度快，谁就趋向于 0的本领高。 （1）lim T X 使用方法: Pn(X) 5、lim — --- = X *Qm （X ） ,n = m b o 0,n V m
V- 巳(X )的最高次幕是n,Q m(x )的最高次幕是m.,只比较最高次幕，谁的次幕高，谁的头大，趋向于无 穷大的速度 n A m,分子以更快的速快。n = m,以相同的比例趋向于无穷大；n < m，分母以更快的速度趋向于无穷大; 度趋向于无穷大。
专升本大学英语阅读理解辅导资料
大学英语阅读理解辅导资料：（共45题） Passage 1 The Antarctic is actually a desert. It is the only continent on the earth without a river or a lake. The Antarctic is all ice all year round. The warmest temperature ever recorded there is zero, at the South Pole. Explorers used to think that a place so cold would have a heavy snowfall. But less than ten inches of snow falls each year. That is less than half an inch of water. Ten times that much moisture falls in parts of the Sahara. The little snow that falls in Antarctica never melts. It continues to pile up deeper and deeper year after year. When the snow gets to be about eighty feet deep it is turned to ice by the weight of the snow above it. 1. Antarctica is called a desert because it ________. A. is sandy B. has the same temperature as a desert C. has little moisture and no lakes or rivers D. All of the above 2. The Antarctic has ________. A. ten times as much moisture as the Sahara B. the same amount of moisture as the Sahara C. about one-tenth the moisture of the Sahara D. None of these. 3. The temperature in the Antarctic is ________. A. always above zero B. always below zero C. never recorded D. Both B and C 4. The snow in Antarctica is very deep because it ________. A. never stops falling B. piles up year after year C. never melts D. Both B and C 5. The snow turns to ice when ________. A. it gets wet B. the temperature gets colder C. the next snowfall comes D. the snow above it is heavy enough 答案：CDBDD Passage 2 Astronomers ( 宇航员) can tell just how hot the surface of the moon gets. The side of the moon toward the sun gets two degrees hotter than boiling water. The night side reaches 243 degrees below zero. In a lunar eclipse (月食) the earth's shadow falls on the moon. Then the moon's temperature may drop 300 degrees in a very short time. A temperature change like this cannot happen on the earth. Why does it happen on the moon? Astronomers know that the surface of the moon is dust. On the earth, rocks store heat from the sun. When the sun goes down, the rocks stay warm. But the dust of the moon cannot store heat. So when the moon gets dark, the heat escapes quickly. The moon gets very cold.