英文版微積分試卷答案

1、精選優(yōu)質(zhì)文檔-----傾情為你奉上專心---專注---專業(yè)1、 (1) 0 . sin 2 lim xxx ?? ?(2) d(arctan ) x ? 21 d 1+ x x(3) 2 1 d sin x x ? ? -cot +C x x(4).. 2 ( ) ( ) x n e ? 2 2n x e(5)26/3 40 1 2 d x x ? ? ?2、 (6) The right propositi

2、on in the following propositions is ___A_____.A. If exists and does not exist then does not exist. lim ( )x a f x? lim ( ) x a g x? lim( ( ) ( ))x a f x g x? ?B. If , do both not exist then does not exist. lim ( )x a

3、 f x? lim ( ) x a g x? lim( ( ) ( ))x a f x g x? ?C. If exists and does not exist then does not exist. lim ( )x a f x? lim ( ) x a g x? lim ( ) ( )x a f x g x?D. If exists and does not exist then does not exist. lim ( )

4、x a f x? lim ( ) x a g x?( ) lim ( ) x af xg x ?(7) The right proposition in the following propositions is __B______.A. If then exists. lim ( ) ( )x a f x f a? ? ( ) f a ?B. Ifthen does not exist. lim ( ) ( )x a f x

5、 f a? ? ( ) f a ?C. If does not exist then . ( ) f a ? lim ( ) ( )x a f x f a? ?D. If does not exist then the cure does not have tangent at . ( ) f a ? ( ) y f x ? ( , ( )) a f a(8) The right statement in the following s

6、tatements is ___D_____. A. B. sin lim 1xxx ?? ?1lim(1 ) xx x e?? ? ?C. D. 1 1 d 1 x x x C ? ??? ? ? ? ? 5 51 1 d d 1 1b ba a x y x y ? ? ? ? ?(9) For continuous function , the erroneous expression in the following expre

7、ssions ( ) f xis ____D__.A.B. d ( ( )d ) ( ) dba f x x f b b ? ?d ( ( )d ) ( ) dba f x x f a a ? ? ?C. D. d ( ( )d ) 0 dba f x x x ? ?d ( ( )d ) ( ) ( ) dba f x x f b f a x ? ? ?(10) The right proposition in the follow

8、ing propositions is __B______.A. If is discontinuous on then is unbounded on . ( ) f x [ , ] a b ( ) f x [ , ] a b精選優(yōu)質(zhì)文檔-----傾情為你奉上專心---專注---專業(yè)6、 Given that . 22 ( ) 1x f x x ? ?(1) Find the intervals on which is increas

9、ing or decreasing. ( ) f xWhen2 2’2 22 1 2 ( ) 1x x x x f x x? ? ? ? ?（）（） 2 221xx ? ? （）’( ) 0 0 f x x ? ? ? ’( ) 0 0 f x x ? ? ?Therefore, the increasing interval is , the decreasing interval is ? ? 0 ? ? ， ? ? 0 ??，(

10、2) Find the local maximum and minimum values of ( ) f xThe function is increasing in interval , decreasing in interval ’( ) 0 0 f x x ? ? ? ? ? 0 ? ? ，, therefore, the function exist the local minimum value, it is? ? 0 ?

11、?， ( ) 0 f x ?(3)Find the intervals of concavity and the inflection points.' 2 2 2 2 4 22 2 2 4 2 42 2 1 8 1 6 4 2 ''( ) 1 1 1x x x x x x f x x x x? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?（）（）（）（）（）4 22 46 4 2 3 3

12、''( ) 0 1 3 3x x f x x or x x? ? ? ? ? ? ? ? ? ? （）4 22 46 4 2 3 3 ''( ) 0 0 0 1 3 3x x f x x or x x? ? ? ? ? ? ? ? ? ? ? ? （）3 3 1 ''( ) ''( )= 3 3 4 f f ? ?Therefore, the concave upward

13、interval are , , the concave downward 33? ? ?? ? ? ? ? ? ? ?， 33? ? ? ? ? ? ? ? ? ?，interval are ,and the inflection points are ,3 - 0 3? ?? ? ? ? ? ?， 3 0 3? ?? ? ? ? ? ?， 3 1 - 3 4? ?? ? ? ? ? ?， 3 13 4? ?? ? ? ? ? ?

14、，(4) Find the asymptote lines of the cure ( ) y f x ?2221 lim = 1 1 1 1+xxxx?? ? ?Therefore, the lineis a horizontal asymptote y = 1（考點：4.3 節(jié)，4.5、4.6 節(jié)。近幾年經(jīng)常會考一道作圖題。這種題目應(yīng)該在注意的點主要包括函數(shù)的定義域，對稱性，增減區(qū)間，極值點，凹凸性，拐點，以及漸近線等。大家參照課本