| 91年 4月13日 16:00 ~ 17:30 企管系乙組 | 誠實是我們珍視的美德， 我們喜愛「拒絕作弊，堅守正直」的你！ |
| 科目：微績分 |
|
1.
|
Evaluate the integrals. (30 %) |
(a) (d)
 |
|
(b)
(e)  |
|
(c) |
|
|
2.
|
Graph the function 
and find its local maximum and minimum values.(10
%) |
|
3.
|
Find the maximum and minimum values of
the function 
on the circle  .
(10 %) |
|
4.
|
Find the consumer's surplus for the demand
function 
at consumption level 
(10 %) |
|
5.
|
Find the area of the region R
bounded by the graphs of 
and  .
(10 %) |
|
6.
|
Find the Maclaurin series of 
(10 %) |
|
7.
|
Suppose $ 10,000 is invested at an annual interest rate of 6%. If the interset is compounded continuousely, compute the balance after |
| 10 years. (10 %) | |
|
8.
|
A manufacturing company determines that the level of production resulting from the use of x units of labor and y units of capital per |
| hour to produce a certain product is given by the production function | |
 |
|
| Each unit of labor costs $ 200 and each unit of capital costs $ 100. If a total of $ 800 worth of labor and capital is to be used per hour, | |
| find the amounts of labor and capital for which production will be a maximum. (10 %) | |
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