課程名稱︰微積分甲上
課程性質︰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（年月日）︰2010/10/28
考試時限（分鐘）：30
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1
A. (5 points) Evaluate∫ [(x/(1+x))^(1/2)] dx
0
┌ x^(2x) if x > 0
B. Let f(x) = │
└ 1 if x = 0
(a) (5 points) Show that lim f(x) exists and f is continuous at x = 0.
x→0
x≠0
(b) (5 points) Find all relative extrema of f.
(c) (5 points) Find all points of inflection of f if there is any.
┌ (x^2)sin(1/x) if x ≠ 0
C. Let f(x) = │
└ 0 if x = 0
(a) (5 points) Show that f is differentiable at x = 0 and find f'(0).
(b) (5 points) Find f'(x) for all x. Is f'(x) continuous?
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