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：理学院
开课系所︰数学系
考试日期（年月日）︰2014.7.9
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 :
Notice: There are 5 problems.
Each problem coonsists of 2 parts and counts 20pts.
(1) (a) For the function defined by setting (10pt)
1+x^2 , x<1
g(x)= 3 , x=1
4-2x , x>1
determine whether the limit lim g(x) exists and if g is continuous at
x→1 x=1.
(b) Show that lim f(x)=0 if and only if lim │f(x)│=0. (10pt)
x→c x→c
(2) (a) Determine the discontinuities, if any, of the following function:(10pt
)
2x+1 , x≦0
f(x)= 1 , 0<x≦1
x^2+1 , x>1
(b)Evaluate the limit if it exists. (10pt)
lim (sinx)^2
x→0