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研究所、轉學考(插大)-微積分
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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
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題組內容
3 Use Taylor formula to find a second degree polynomial approximation of f near the given point.
(a)f (x)=x
4
+x
3
+x
2
+x+1 , near a = 2 . (8%)
其他申論題
(a) (8%)
#498914
(b) (8%)
#498915
(a) (8%)
#498916
(b) (8%)
#498917
(b) f( x，y)=exln(1+y ),nare( a,b)=(0,0) . (8%)
#498919
4 Solve the differential equation , y(0) = 1. (8%)
#498920
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%)
#498921
6 Find the direction in which f(x，y)=x2y+exyincreases and decreases most rapidly at the point (1,0). Then find the derivatives of f in these directions. (8%)
#498922
7 Find the maximum value of the functionf(x，y)=xy-x2-y2-2x-2y+4 (8%)
#498923
8.Find the maximum and minimum values of the functionf(x，y)=x2+y2 subject to the constraint x2-2x+y2-4y=0 . (10%)
#498924
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