課程名稱︰微積分甲下
課程性質︰數學系大一必帶
課程教師︰陳榮凱
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/03/27
考試時限（分鐘）：30
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
The total is 25 points.
(1) (8 pts) Expand the function f(x + h, y + k) in powers of h, k up to degree
π
3 for f(x, y) = cos(x + 2y) at (x, y) = (0, －).
２
x x
(2) (9 pts) Consider L = (y e + sin y) dx + (e + x cos y) dy. Determine
whether L = df for some function f or not. If it is, find f.
2 2
(x - y ) dx - 2xy dy
(3) (8 pts) Consider L = ────────── and γ the circle of radius
2 2 2
(x + y )
starting from (2, 0) clockwise. Evaluate ∫L.
γ