电大经济数学基础参考答案3-1（微分电大参考答案）-2022电大专科考试参考答案.doc

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电大经济数学基础参考答案3-1(微分完整版电大参考答案)-2022电大专科考试参考答案

5
经济数学基本微分函数
一、单项选择题
1．函数的界说域是（ D ）． &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp;A． B． C． D． 且
2．若函数的界说域是[0，1]，则函数的界说域是( C )．
A． &nbsp;B． &nbsp; &nbsp;C． &nbsp; &nbsp; &nbsp; &nbsp;D
3．下列各函数对中，（ D ）中的两个函数相等．
&nbsp; &nbsp;A．， B．，+ 1
&nbsp; &nbsp;C．， &nbsp;D．，
4．设，则=（ A ）．
&nbsp; &nbsp;A． &nbsp; &nbsp;B． &nbsp;C． &nbsp; &nbsp; &nbsp;D．
&nbsp; &nbsp;5．下列函数中为奇函数的是（ C ）．
A． &nbsp; B． &nbsp; C． &nbsp; D．
&nbsp; &nbsp;6．下列函数中，（ C ）不是根基初等函数．
&nbsp; &nbsp;A． &nbsp; B． &nbsp; C． D．
7．下列结论中，（ C ）是正确的． &nbsp; &nbsp;
&nbsp; &nbsp;A．根基初等函数都是单调函数 &nbsp; &nbsp; B．偶函数的图形关于坐标原点对称
&nbsp; &nbsp;C．奇函数的图形关于坐标原点对称 &nbsp; &nbsp; D．周期函数都是有界函数
8. 那时，下列变量中（　B &nbsp; ）是无限年夜量．
　　A.　 &nbsp; &nbsp; &nbsp; &nbsp; B. &nbsp; &nbsp; &nbsp;　C. 　　　 &nbsp; &nbsp;D.
&nbsp; &nbsp;9. 已知，当（　A &nbsp; ）时，为无限小量.
　　A. 　 &nbsp; &nbsp;B. &nbsp; 　C. 　　 &nbsp;D.
10．函数 在x = 0处持续，则k = ( A )．
A．-2 &nbsp; &nbsp; B．-1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; C．1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; D．2
&nbsp; &nbsp;11. 函数 在x = 0处（　B &nbsp; ）．
　　A. 左持续　 &nbsp; &nbsp; &nbsp; &nbsp;B. 右持续 &nbsp; &nbsp; &nbsp;　　C. 持续　　　 &nbsp; &nbsp;D. 摆布皆不持续
&nbsp; &nbsp;12．曲线在点（0, 1）处的切线斜率为（ &nbsp;A &nbsp; &nbsp;）
&nbsp;A． &nbsp; &nbsp; &nbsp;B． &nbsp; &nbsp;C． &nbsp; &nbsp; &nbsp; &nbsp; D．
13. 曲线在点(0, 0)处的切线方程为（　A &nbsp; ）．
　　A. y = x　 &nbsp; &nbsp; &nbsp; &nbsp; B. y = 2x &nbsp; &nbsp; &nbsp;　　C. y = x　　　 &nbsp; &nbsp;D. y = -x
&nbsp; &nbsp;14．若函数，则=（ &nbsp;B ）．
&nbsp; &nbsp;A． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; B．- &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; C． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;D．-
&nbsp; &nbsp;15．若，则（ &nbsp; D &nbsp; ）．
&nbsp; &nbsp;A． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; B．
&nbsp; &nbsp;C． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;D．
&nbsp; &nbsp;16．下列函数在指定区间上单调增加的是（ &nbsp;B ）．
&nbsp; &nbsp;A．sinx &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;B．e x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;C．x 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; D．3 - x
&nbsp; &nbsp;17．下列结论正确的有（ &nbsp;A &nbsp; ）．
&nbsp; &nbsp;A．x0是f (x)的极值点，且(x0)存在，则必有(x0) = 0
&nbsp; &nbsp;B．x0是f (x)的极值点，则x0必是f (x)的驻点
&nbsp; &nbsp;C．若(x0) = 0，则x0必是f (x)的极值点
&nbsp; &nbsp;D．使不存在的点x0，必定是f (x)的极值点
&nbsp; &nbsp;18. 设需求量q对价钱p的函数为，则需求弹性为Ep=（ &nbsp;B &nbsp; &nbsp;）．
A． B． &nbsp;C． &nbsp; &nbsp; D．
19．函数的界说域是（D ）． &nbsp; &nbsp; &nbsp; &nbsp;
A． B． &nbsp;C． D． 且
20．函数的界说域是（ C &nbsp;）。
A． &nbsp;B． &nbsp; &nbsp;C． &nbsp; &nbsp; &nbsp; &nbsp;D
21．下列各函数对中，（ D ）中的两个函数相等．
A．， B．，+ 1
C．， D．，
22．设，则=（ C ）．
A． &nbsp; &nbsp; &nbsp; B． &nbsp; &nbsp; &nbsp; &nbsp;C． &nbsp; &nbsp; &nbsp; &nbsp;D．
23．下列函数中为奇函数的是（ C ）．
A． &nbsp; B． &nbsp;
C． &nbsp; D．
24．下列函数中为偶函数的是（ D ）．
A． &nbsp;B． &nbsp;C． D．
25. 已知，当（　A &nbsp; ）时，为无限小量.
A. 　 &nbsp; &nbsp;B. &nbsp; 　C. &nbsp; D.
26．函数 在x = 0处持续，则k = (A )．
A．-2 &nbsp; &nbsp; B．-1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; C．1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; D．2
&nbsp; &nbsp;27. 函数 在x = 0处持续，则（A &nbsp;）．
A. 1　 &nbsp; &nbsp; &nbsp; &nbsp;B. 0 &nbsp; &nbsp; &nbsp;　　C.　2　　 &nbsp; &nbsp;D. &nbsp;
28．曲线在点（0, 1）处的切线斜率为（ A &nbsp; &nbsp; ）．
A． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;B． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;C． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; D．
29. 曲线在点(1, 2)处的切线方程为（　B &nbsp; ）．
A. &nbsp; &nbsp; &nbsp; &nbsp; B. &nbsp; &nbsp; &nbsp;　
C. 　　　 &nbsp; &nbsp;D. &nbsp;
30．若函数，则=（ &nbsp;B ）．
&nbsp; &nbsp;A． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; B．- &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; C． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;D．-
31．下列函数在指定区间上单调削减的是（ &nbsp;D ）．
A．sinx &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;B．e x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;C．x 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; D．3 – x
&nbsp; &nbsp;32．下列结论正确的有（ &nbsp;A &nbsp; ）．
&nbsp; &nbsp;A．x0是f (x)的极值点，且(x0)存在，则必有(x0) = 0
&nbsp; &nbsp;B．x0是f (x)的极值点，则x0必是f (x)的驻点
&nbsp; &nbsp;C．若(x0) = 0，则x0必是f (x)的极值点
D．使不存在的点x0，必定是f (x)的极值点
&nbsp; &nbsp;33. 设需求量q对价钱p的函数为，则需求弹性为Ep=（ &nbsp;B &nbsp; &nbsp;）．
A． &nbsp; &nbsp;B． &nbsp; &nbsp;C． D．
二、填空题
1．函数的界说域是 [-5，2]
2．函数的界说域是 (-5, 2 )
3．若函数，则
4．设函数，，则
5．设，则函数的图形关于　　y轴 &nbsp;　　　对称．
6．已知出产某种产物的成本函数为C(q) = 80 + 2q，则当产量q = 50时，该产物的平均成本为3.6
7．已知某商品的需求函数为q = 180 – 4p，其中p为该商品的价钱，则该商品的收入函数R(q) = 45q – 0.25q 2
8. 　　　1　　　.
9．已知，那时，为无限小量．
　　10. 已知，若在内持续
，则　　2　 &nbsp;.
　　11. 函数的间断点是
12．函数的持续区间是，，
13．曲线在点处的切线斜率是
14．函数y = x 2 + 1的单调增加区间为(0, +)
15．已知，则= 　　　0　　　．
16．函数的驻点是
17．需求量q对价钱的函数为，则需求弹性为
&nbsp; &nbsp;18．已知需求函数为，其中p为价钱，则需求弹性Ep =
19．函数的界说域是 ．谜底：(-5, 2 )
20．若函数，则．谜底：
21．设，则函数的图形关于　　对称．谜底：y轴
22．已知，当 &nbsp; &nbsp; 时，为无限小量．谜底：
23．已知，若在内持续
则　 &nbsp;. 谜底2
24．函数的间断点是　　　．谜底：
25. 函数的持续区间是 ．谜底：
26．曲线在点处的切线斜率是 ．谜底：．
27. 已知，则= 　　　　　　．谜底：0
28．函数的单调增加区间为 ．谜底：（
29. 函数的驻点是　　 &nbsp; &nbsp;　 &nbsp; 　. 谜底：
30．需求量q对价钱的函数为，则需求弹性为 。
谜底：
三、计较题
1． &nbsp; &nbsp; 1．解 &nbsp; = = &nbsp;= &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
2．
2．解：= &nbsp;
=
3． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp;3．解 &nbsp;= &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ==22 = 4 &nbsp;
4．
4．解 &nbsp;=
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= = 2 &nbsp;
5． &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
5．解 &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
6．
6．解 &nbsp;= &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =
7．已知，求 ．
7．解：(x)==
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =
8．已知，求 ．
8．解 &nbsp;
9．已知，求；
9．解 &nbsp;由于
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 所以 &nbsp; &nbsp;
10．已知y =，求 ． &nbsp;
10．解 &nbsp;由于 &nbsp;
所以 &nbsp;
11．设，求．
11．解 &nbsp;由于 &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
所以 &nbsp;
12．设，求．
12．解 &nbsp;由于 &nbsp;
所以 &nbsp;
13．已知，求 ．
13．解 &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
14．已知，求 ．
14．解：
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
15．由方程确定是的隐函数，求．
　 &nbsp;15．解 &nbsp;在方程等号双方对x求导，得
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
故 &nbsp; &nbsp; &nbsp;
　16．由方程确定是的隐函数，求.
16．解 &nbsp;对方程双方同时求导，得
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=.
17．设函数由方程确定，求．
17．解：方程双方对x求导，得 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
那时，
&nbsp; &nbsp; &nbsp;所以，
18．由方程确定是的隐函数，求．
18．解 &nbsp;在方程等号双方对x求导，得
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
故 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
19．已知，求 ．
解：
20．已知，求
解：． &nbsp;
21．已知，求；
解：
22．已知，求dy ．
解： &nbsp;
dy=
23．设 y，求dy．
解：

24．设，求．
&nbsp;解：

四、应用题
&nbsp; &nbsp;1．设出产某种产物个单元时的成本函数为：（万元）,
求：（1）那时的总成本、平均成本和边际成本；
&nbsp; &nbsp; &nbsp; &nbsp;（2）当产量为若干好多时，平均成本最小？ &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp;1．解（1）由于总成本、平均成本和边际成天职袂为：

， &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp;所以，
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;，
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; （2）令 ，得（舍去）由于 是其在界说域内独一驻点，且该问题的确存在最小值，所以当20时，平均成本最小. &nbsp;
2．某厂出产一批产物，其固定成本为2000元，每出产一吨产物的成本为60元，对这种产物的市场需求纪律为（为需求量，为价钱）．
试求：（1）成本函数，收入函数； &nbsp; &nbsp; （2）产量为若干好多吨时利润最年夜？
2．解 &nbsp;（1）成本函数= 60+2000．
&nbsp; &nbsp;由于 &nbsp;，即，
&nbsp; &nbsp;所以 &nbsp;收入函数==()=． &nbsp;
&nbsp; &nbsp;（2）由于利润函数=- =-(60+2000)
= 40--2000
且 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=(40--2000=40- 0.2
令= 0，即40- 0.2= 0，得= 200，它是在其界说域内的独一驻点．
&nbsp; &nbsp;所以，= 200是利润函数的最年夜值点，即当产量为200吨时利润最年夜．
3．设某工场出产某产物的固定成本为50000元，每出产一个单元产物，成本增加100元．又已知需求函数，其中为价钱，为产量，这种产物在市场上是畅销的，试求：（1）价钱为若干好多时利润最年夜？（2）最年夜利润是若干好多？
3．解 （1）C(p) = 50000+100q = 50000+100(2000-4p)
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =250000-400p
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;R(p) =pq = p(2000-4p)= 2000p-4p 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
利润函数L(p) = R(p) - C(p) =2400p-4p 2 -250000，且令 &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =2400 – 8p = 0
得p =300，该问题的确存在最年夜值. 所以，当价钱为p =300元时，利润最年夜. &nbsp;
（2）最年夜利润 （元）
4．某厂出产某种产物q件时的总成本函数为C(q) = 20+4q+0.01q2（元），单元发卖价钱为p = 14-0.01q（元/件），试求：（1）产量为若干好多时可使利润达到最年夜？（2）最年夜利润是若干好多？ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4．解 &nbsp;（1）由已知
利润函数
则，令，解出独一驻点.
由于利润函数存在着最年夜值，所以当产量为250件时可使利润达到最年夜， &nbsp; &nbsp;
（2）最年夜利润为
&nbsp; （元
&nbsp; &nbsp; 5．某厂每天出产某种产物件的成本函数为（元）.为使平均成本最低，每天产量应为若干好多？此时，每件产物平均成本为若干好多？
&nbsp; &nbsp; 5. 解 &nbsp;由于 == &nbsp;（） &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;== &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; 令=0，即=0，得=140，= -140（舍去）.
=140是在其界说域内的独一驻点，且该问题的确存在最小值. &nbsp;
&nbsp; &nbsp; 所以=140是平均成本函数的最小值点，即为使平均成本最低，每天产量应为140件. 此时的平均成本为
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;==176 &nbsp;（元/件） &nbsp; &nbsp;
&nbsp; &nbsp;6．已知某厂出产件产物的成本为（万元）．问：要使平均成本起码，应出产若干好多件产物？ &nbsp; &nbsp; &nbsp; &nbsp;
6．解 （1） 由于 &nbsp;== &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; == &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp;令=0，即，得=50，=-50（舍去），
&nbsp; &nbsp;=50是在其界说域内的独一驻点．
&nbsp; &nbsp;所以，=50是的最小值点，即要使平均成本起码，应出产50件产物．
7．设出产某种产物个单元时的成本函数为：（万元）,
求：（1）那时的总成本、平均成本和边际成本；
&nbsp; &nbsp; （2）当产量为若干好多时，平均成本最小？
解（1）由于总成本、平均成本和边际成天职袂为：

， &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp;所以，
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;，
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; （2）令 ，得（舍去）
&nbsp; &nbsp; &nbsp;由于是其在界说域内独一驻点，且该问题的确存在最小值，所以当20时，平均成本最小. &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; 8．某厂出产某种产物q件时的总成本函数为C(q) = 20+4q+0.01q2（元），单元发卖价钱为p = 14-0.01q（元/件），问产量为若干好多时可使利润达到最年夜？最年夜利润是若干好多.
解 &nbsp;由已知
利润函数
则，令，解出独一驻点.
由于利润函数存在着最年夜值，所以当产量为250件时可使利润达到最年夜， &nbsp; &nbsp;
且最年夜利润为
&nbsp; &nbsp; （元）
&nbsp;9．某厂每天出产某种产物件的成本函数为（元）.为使平均成本最低，每天产量应为若干好多？此时，每件产物平均成本为若干好多？
解 &nbsp;由于 == &nbsp;（） &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;== &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp;令=0，即=0，得=140，= -140（舍去）.
=140是在其界说域内的独一驻点，且该问题的确存在最小值. &nbsp;
&nbsp; &nbsp; &nbsp; 所以=140是平均成本函数的最小值点，即为使平均成本最低，每天产量应为140件. 此时的平均成本为
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;==176 &nbsp;（元/件） &nbsp;
10．某厂出产一批产物，其固定成本为2000元，每出产一吨产物的成本为60元，对这种产物的市场需求纪律为（为需求量，为价钱）．试求：
&nbsp; &nbsp; （1）成本函数，收入函数； &nbsp; &nbsp;
（2）产量为若干好多吨时利润最年夜？
解 （1）成本函数= 60+2000．
&nbsp; &nbsp; 由于 &nbsp;，即，
&nbsp; &nbsp; 所以 &nbsp;收入函数==()=． &nbsp;
&nbsp; &nbsp; （2）由于利润函数=- =-(60+2000)
= 40--2000
且 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=(40--2000=40- 0.2
令= 0，即40- 0.2= 0，得= 200，它是在其界说域内的独一驻点．
&nbsp; &nbsp; 所以，= 200是利润函数的最年夜值点，即当产量为200吨时利润最年夜．

精品电年夜复习资料14</p>