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）︰2010/10/21
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 :
A. (a) (5 points) State the Weierstrass principle in real number system.
(b) (5 points) Use the Weierstrass principle to show that every bounded
monotonic increasing sequence in R is convergent.
B. (10 points) Suppose u(x) > 0 and v(x) > 1 are two dierentiable functions
on R. Find the derivative of the function
f(x) = log u(x) in terms of u, v, u' and v'.
v(x)
-1 -1
C. (10 points) Let f(x) = sinh (cosh x), where sinh is the
inverse of hyperbolic sine function. Find f'(x).
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