課程名稱︰微積分甲上
課程性質︰必修
課程教師︰張鎮華老師
開課學院：電資學院、管理學院等等
開課系所︰經濟系、材料系、電機系、資工系等等
考試日期（年月日）︰ 101 年 9 月 24 日
考試時限（分鐘）： 30 分鐘
是否需發放獎勵金：是，謝謝您 =)
（如未明確表示，則不予發放）
試題 :
2
1.(30%) Use an ε－δ definition to prove that lim (x + x +1) = 7.
x→2
2.(30%) Suppose that f and g are continuous at c. Prova that if f(c) < g(c),
then there exists δ>0 such that f(x) < g(x) for all x∈(c-δ, c+δ). Is it
true that "if f(c)≦g(c), then there exists δ>0 such that f(x)≦g(x) for
all x∈(c-δ,c+δ)"? If it is true then prove it, otherwise give a
counterexample to disprove it.
3.(40%) Consider the function f defined by
╭3x+a, x<2;
║
f(x) = ╢b, x=2;
║ 2
╰2x +1, x>2,
where a and b are constants. Determine a and b for which lim f(x) exists,
x→2-
for which lim f(x) exists, for which lim f(x) exists, for which f is
x→2+ x→2
continous at 2.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.239.113