課程名稱︰微積分甲上
課程性質︰必修
課程教師︰張鎮華
開課學院：電資學院等甲一
開課系所︰以上
考試日期（年月日）︰ 101 年 10 月 8 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 2 2 2 2
1.(40%) The curve (x + y ) = x － y is called a lemniscate, whose graph is
shown as below. Find the four points of the curves at which the tangent line
is horizontal. Figure is here: http://ppt.cc/Pfkp
╭ xsin(1/x), x≠0
2.(60%) Let f(x) = ╢ and g(x) = xf(x). The graphs of f and g
╰ 0, x＝0
are shown as below. Answer the following quetions, you need to justify
your answers.
(a) Determine all x∈(-∞,∞) for which f(x) (resp. g(x)) is continous.
(b) Determine all x∈(-∞,∞) for which f'(x) (resp. g'(x)) exists. Find
the derivative.
(c) Determine all x∈(-∞,∞) for which f'(x) (resp. g'(x)) is continous.
Figure is here: http://ppt.cc/ahln
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