所屬科目：研究所、轉學考(插大)-微積分
1. Find the limit.
2. Find (x sin x).
3. Evaluate the integral
4. Evaluate the integral dydx.
6. Let y = (sin a)x, sin x ＞ 0. Find
7. Assume that constants a and b are positive. Find equations for all horizontal asymptotes for the graph of .
8. We say that the two commodities are substitute commodities if a decrease in the demand for one results in an increase in the demand for the other. Con- versely, two commodities are referred to as complementary commodities if a decrease in the demand for one results in a decrease in the demand for the other as well. Suppose that the demand equations that relate the quantities demanded x and y to the unit prices p and q of the commodities A and B respectively are given by . Are A and B substitute, complementary or neither?
(b)(4分)Find f'(x) for x≠0.
(a) (6 分) Use the integral test to determine if the seriesconverges or diverges.
(b) (6 分) Find all values of x for which converges absolutely.
3. Suppose a units of labor and y units of capital are required to produce units of a certain product. If each unit of labor costs $200, each unit of capi- tal costs $300, and a total of $60,000 is available for production, determine how many units of Iabor and how many units of capital should be used to maximize production.
阿摩線上測驗
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阿摩線上測驗
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(x sin x).
dydx.
.
. Are A and B substitute, complementary or neither? 
converges or diverges.
converges absolutely. 
units of a certain product. If each unit of labor costs $200, each unit of capi- tal costs $300, and a total of $60,000 is available for production, determine how many units of Iabor and how many units of capital should be used to maximize production.