課程名稱︰微積分甲上
課程性質︰暑修
課程教師︰周青松
開課學院：理學院
開課系所︰
考試日期（年月日）︰2009/7/15
考試時限（分鐘）：
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Show that:
A). sin x
lim ──── ＝ 1
x→0 x
B). 1－cos x
lim ───── ＝ 0
x→0 x
2. Find the indicated derivatives
A). d d^2
──[t^2 ───(tcos 3t)]
dt dt^2
B). d d
──[t ──cos t^2]
dt dt
3.
A). Find the intervals on which f increases and the intervals on which f
decreases, where
｛ x^3, x＜1
f(x)＝ 1
｛──x＋2, x≧1
2
B). Set f(x) ＝ sec^2 x and g(x) ＝ tan^2 x on the interval (-π/2,π/2).
Show that f'(x) ＝ g'(x) for all x ∈ (-π/2,π/2).
4.
A). Determine A and B so that the curve
y ＝ Ax^(1/2)＋Bx^(-1/2)
has a point of inflection at (1,4).
B). Determine A and B so that the curve
y = Acos 2x ＋ Bsin 3x
has a point of inflection at (π/6,5).
1 7
5. Sketch the graph of f(x) ＝ ──x^4－2x^2＋── on the interval (-∞,3].
4 4
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※ 編輯: nanmadol 來自: 140.112.199.90 (07/16 05:21)