→ ilway25:第一題沒打完整 08/21 22:05
※ 編輯: YYPPOO 來自: 61.220.183.235 (08/21 23:48)
→ YYPPOO:感謝指正呵 ^^a 08/21 23:49
課程名稱︰微積分甲下
課程性質︰
課程教師︰周青松
開課學院：
開課系所︰
考試日期（年月日）︰2008/08/21
考試時限（分鐘）：110min
是否需發放獎勵金：是！
試題 :
I.
A). Given that f is continuous, use L'Hopital's rule to determine
1 x
lim (─ ∫ f(t) dt )
x→0 x 0
B). Calculate
1 x t^2
lim (─ ∫ e dt )
x→∞ x 0
II.
A). Find
x^(-1)
lim (1+x)
x→0+
B). Show that, for each real x,
n x
lim (1+(x/n)) = e
n→∞
III.
Prove that, if f is contimuous, positive, and decreasing on [1,∞), then
∞ ∞
Σ f(k) converges iff ∫ f(x)dx converges
k=1 1
IV.
Let Σak be a series with nonnegative terms, and suppose that
k^(-1)
(ak) → ρ
Show that,
A). if ρ<1, then Σak converges.
B). if ρ>1, then Σak diverges.
V.
Find a power series representation for the improper integral:
A).
x 1 - cost
∫ ───── dt
0 t^2
B).
x cosh t
∫ ──── dt
0 t
(每大題均20分)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.102.7