作者  ajenny13 (~~~)                                          看板  NTU-Exam 
 標題  [試題] 103-1 周青松 微積分甲上 第二次小考                              
 時間  Wed Dec 10 09:38:22 2014                                               
───────────────────────────────────────

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


--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.112.236.43
※ 文章網址: http://www.ptt.cc/bbs/NTU-Exam/M.1418175505.A.CF8.html