课程名称︰微积分甲上 课程性质︰大一共同必修 课程教师︰张志中 开课学院：工学院 开课系所︰数学系 考试日期（年月日）︰ October 21,2008 考试时限（分钟）：一节课 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.Evaluate the following limits, if it exists. If the limit does not exist, explain why. (a) (10 points) t^2-9 lim ────── t→-3 2t^2+7t+3 (b) (10 points) x^2-1 lim ──── x→1 │x-1│ 2.Evaluate f'(1) of the following functions. (a) (10 points) f(x)= (x(x-2)(x^2+1)^(-1))^(1/3) 题目是用分式写 (b) (10 points) f(x)=arcsin(√2x/2) 3. f(x)={ x^3sin(1/x) ,when x≠0 0 ,when x=0 (a) (10 points) Does lim x→0 f(x) exist? If so, what is it? If NOT ,why not? (b) (10 points) Is f(x) differentiable at x=0? If so, explain your reason and compute f'(0) If NOT, why not? 4.f(x)={ x+b , when x<0 cosx-b, when x>=0 (a) (10 points) Does there exist a number b such that f(x) is continuous at x=0? (b) (10 points) Does there exist a number b such that f(x) is differential at x=0? Give reason for your answers. 5.(20 points) Show that : If (Xo,Yo) is a point on the graph of 2 2 X Y ──+──=1 a^2 b^2 , then the tangent line which passes through (Xo,Yo) is Xo*X Yo*Y ───+─── = 1 . a^2 b^2 ※ 编辑: chihyanglee 来自: 140.112.233.26 (10/28 22:08)