课程名称︰微积分乙上 课程性质︰必修 课程教师︰李聪成 开课学院：社科院、管院、理学院 开课系所︰经济、财金、国企、工管、会计、地理 考试日期（年月日）︰2011年11月10日 考试时限（分钟）：120分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 请将每一步骤表达清楚,不可以只写答案。 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 (抛物线). 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 (发射) 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 (长,宽) of the rectangle of maximum possible area that can be inscribed (内接) in a semicircle of radius 4. 参考答案： 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) 用书：Soo T. Tan, Calculus, 2010, Cengage Learning 范围： Ch1 Limits Ch2 The Derivative Ch3 Applications of the Derivative ※ 编辑: mickeyhp 来自: 220.136.82.27 (01/22 14:39)