98年 - 98 東吳大學轉學生(含進修學士班)招生考試試題_經濟學系二年級：微積分#116770

科目：研究所、轉學考(插大)-微積分 | 年份：98年 | 選擇題數：0 | 申論題數：12

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (12)

(a) (8%)

(b) (8%)

(a) (8%)

(b) (8%)

(a)f (x)=x⁴+x³+x²+x+1 , near a = 2 . (8%)

(b) f( x，y)=e^xln(1+y ),nare( a,b)=(0,0) . (8%)

4 Solve the differential equation , y(0) = 1. (8%)

5 Find when r = 1 , s = −1,

if w= (x+y+z)2, x= r−s , y= cos(r + s) , z= sin(r+ s ) . (8%)

6 Find the direction in which f(x，y)=x²y+e^xyincreases and decreases most rapidly at the point (1,0). Then find the derivatives of f in these directions. (8%)

7 Find the maximum value of the function

f(x，y)=xy-x²-y²-2x-2y+4 (8%)

8.Find the maximum and minimum values of the functionf(x，y)=x²+y² subject to the constraint x²-2x+y²-4y=0 . (10%)

9 A business sells 20000 units of product per week at a price of $16 each. It can sell 2000 more units per week for each $1 reduction in price. What price per unit will maximize the weekly revenue? (10%)