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）︰103年10月24日
考試時限（分鐘）：50分鐘
試題 :
(1)(25 pts)
Find A and B such that the function f is differentiable at x=2
f(x) = {x^2-2, x≦2
{Bx^2+Ax, x>2
(2)(25pts)
Show that f is not differentiable at 0, g is differentiable at 0
f(x) = {x, x∈rational
{0, x∈irrational
g(x) = {x^2, x∈rational
{0, x∈irrational
(3)(25pts)
Find A and B such that
the derivative of f is continuous
f(x) = {Ax^2+B, x<-1
{Bx^5+Ax+4, x≧-1
(4)(25pts)
Let f be differentiable show that
(a)if f is even then f' is odd
(b)if f is odd then f' is even