課程名稱︰微積分甲上
課程性質︰必修
課程教師︰周青松
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014.7.9
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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