課程名稱︰微積分甲下
課程性質︰大一共同必修
課程教師︰薛克民
開課學院：生農學院,理學院,管理學院
開課系所︰生機系,生工系,工管系(科管組),地質系等
考試日期（年月日）︰97/4/6
考試時限（分鐘）：30mins
是否需發放獎勵金：YES
（如未明確表示，則不予發放）
試題 :
1.Find the Maclaurin series for ln(1+x) and find the radius of convergence
(10 points)
2.
(a)Find the Maclaurin series expansion for 1/√ (1-x^2).
(10 points)
-1
(b)Use part (a) to find the Maclaurin series for sin_ x.
(10 points)
→ →
3.Find the unit tangent vector T(t) for the curve: r(t) = (4√t,t^2,t) at
→
r(1) = (4.1.1).
(10 points)
→ t -t
4.Find the length of the curve r(t) = (√(2t),e ,e ), 0≦t≦1
(10 points)
5.Use polar coordinates to find the following limit :
x^3+y^3
lim ────
(x,y)→(0,0) x^2+y^2
(10 points)
rθ
6.Consider u(r,θ)= e sinθ. Find
(以p表示偏微分符號)
pu
(a) ─ (5 points)
pr
pu
(b) ─ (5 points)
pθ
p^2 u
(c) ─── (5 points)
pr^2
p^2 u
(d) ─── (5 points)
pθ^2
p^2 u
(e) ─── (5 points)
pθpr
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