课程名称︰微积分乙上 课程性质︰选修 课程教师︰陈鹏文 开课学院： 开课系所︰ 考试日期（年月日）︰101.07.09 考试时限（分钟）：110 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Read This First ! Please read each question carefully. Show ALL work clearly in the space provided. In order to receive full credit on a problem, solution methods must be complete, logical and understandable. Answers must be clearly labeled in the spaces provided after each question. Please mark out or fully erase any work that you do not wand graded. The point value of each question is indicated after its statement. No books or other references are permitted. 2x+1 1. Compute lim(----------)^x x→∞ 2x-1 √(x^3+x^2+1) + x 2. Compute lim ----------------- x→-1 x+1 3. Find the first and second derivatives dy/dx and d^2y/dx^2 of x^2 + xy - y^2 = 4 at (2,2). d 4. Compute --- ((x^2 + 1)^3lnx) dx 5. Let y=x^4 - 2x^2. (a) Find the local maximum and local minimum. (b) In which intervals x is the function f concave upward and concave downward? (c) Find all the inflection points. (d) Sketch the graph of f(x) for -2≦x≦2. Find the global maximum and the global minimum. 6. Simplify Let f(x)=cos(csc^(-1)x) for x≧1. Simplify f(x) (so that no inverse function appear in your expression). Also find the derivative of f(x). ln secx 7. Compute the limit lim ------------ x→0 2 tan^2(x) 8. Compute the derivative of f(x). (a) f(x)=(x^2 - 1)^0.5 * e^(x^3) * sec^4(x) sin 2x (b) f(x)= ------------- 1 + cos 2x --

※ 发信站: 批踢踢实业坊(ptt.cc), 来自: 61.230.129.56 ※ 文章网址: http://webptt.com/cn.aspx?n=bbs/NTU-Exam/M.1404540221.A.5ED.html ※ 编辑: d3osef (61.230.129.56), 07/05/2014 14:04:32