课程名称︰微积分甲上 课程性质︰必修 课程教师︰周青松 开课学院：管理学院、生农学院、理学院 开课系所︰工管系科管组、生机系、生工系、地质系 考试日期（年月日）︰2010/11/8 考试时限（分钟）：110分钟 是否需发放奖励金：是 试题 : Warning : Each part from I - V is of 20 points. Please write down your answer in the answer sheets in detail as well as possible. I. ｜1+x^2 , x<1 A. Evaluate lim f(x) if it exists, where f(x)=｜ 3 , x=1 x→1　　　　　　　　　　　　　　　｜4-2x , x>1 B. Give that g(x)=x^2-4x, evaluate the following limit if that exists. g(x)-g(2) lim －－－－－－. x→3 x-3 II. A. Determine the discontinuties, if any, of the following function ｜2x+1 ,x<=0 f(x)=｜ 1 ,0<x<=1. 　　　　　　　　　　｜x^2+1 ,x>1 B. Prove that sinx lim－－－－ = 1. x→0 　x III.　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 　　　　　　　　　　　　　　　　　　　　　　　 　x　　 　1 A. Find the drivative of the function f(x)=（－－－－）^－ . 1+x^2 2 B. Find the second derivative of the function y=x^1/2(tanx^1/2). IV. A. Suppose that f is differentiable on the interior of an interval I and continuous on all of I. Prove that (i)If f'(x)>0 for all x in the interior of I, then f increases on all of I. (ii)If f'(x)<0 for all x in the interior of I, then f decreases on all of I. (iii)If f'(x)=0 for all x in the interior of I, then f is constant on all of I. B. For the function ｜x^3 ,x<1 f(x)=｜ , determine the intervals on which f decreases and the 　　 ｜1/2x+2 ,x=>1 intervals on which f decreases. V.Sketch the graph of f(x)=1/4x^4-2x^2+7/4 on [-5,5]. --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 140.112.241.80 ※ fanif:转录至看板 NTUBIME104HW 10/28 21:35