課程名稱︰微積分乙上
課程性質︰必修
課程教師︰李聰成
開課學院：社科院、管院、理學院
開課系所︰經濟、財金、國企、工管、會計、地理
考試日期（年月日）︰2011年11月10日
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
請將每一步驟表達清楚,不可以只寫答案。
1.Evaluate the limit.
√(5-x) -2
lim ───────
x→1 √(2-x) -1
2.Evaluate the limit.
1
lim x sin ──
x→+∞ x
3.Evaluate the limit.
sin[(3+x)^2]-sin9
lim ──────────
x→0 x
4.Sketch the graph of the given function, making use of any suitable
information you can obtain from the function and its first and second
derivatives.
x^2
f(x) = ─────
x^2 -1
5.Find equations of the lines passing through thepoint (3,2) that are tangent
to the parabola (拋物線).
y=x^2-2x
6.Find and equation of the tangent line to the curve at the point
(-1,[3√(3)]/2).
x^2 y^2
── + ── = 1
4 9
7.Suppose f is defined on R=(-∞,+∞) and satisfies |f(x)-f(y)|≦(x-y)^2 for
all x and y. Show that f is a constant function on R.
8.Find all value(s) of a such that f is continuous on R.
╭ x+1 if x≦a
f(x)=〈
╰ x^2 if x>a
9.At a distance of 12,000 feet from the launch (發射) site, a spectator is
observing a rocket being launched vertically. What is the speed of the rocket
at the instant when the distance of the rocket from the spectator is 13,000
ft and is increasing at the rate of 480 ft/sec ?
10.Find the dimensions (長,寬) of the rectangle of maximum possible area that
can be inscribed (內接) in a semicircle of radius 4.
參考答案：
1.1/2 2.1 3.6cos9 4.略 5.y=2x-4,y=6x-16 6.y=[√(3)/2]x+2√(3)
7.略 8.[1±√(5)]/2 9.1248 10.2√(2)×4√(2)
用書：Soo T. Tan, Calculus, 2010, Cengage Learning
範圍：
Ch1 Limits
Ch2 The Derivative
Ch3 Applications of the Derivative
※ 編輯: mickeyhp 來自: 220.136.82.27 (01/22 14:39)