課程名稱：微積分甲上
課程性質：數學系必修
課程教師：王金龍
開課學院：理學院
開課系所：數學系
考試日期：2010年09月23日
考試時限：30分鐘
是否需發放獎勵金：是
A. (10 points) Consider the function f(x) = x^3 on R and a fixed point a∈R.
Given an ε>0, and a δ>0 s.t. |f(x)-f(a)|<ε whenever |x-a|<δ.
B. (10 points) Suppose that f is continuous at a and f(a) < 0. Show that there
exists an open interval I containing a s.t. f(x) < 0 for all x∈I.
C. (10 points) Show that the function
╭ 0 if x is irrational or x = 0
f(x) =┤
╰ 1/q if x = p/q rational in lowest terms
is discontinuous at x=1.
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