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)