作者wheata (仙人指路不用钱)
看板NTU-Exam
标题[试题] 99上 王金龙 微积分甲上 第五次小考
时间Thu May 26 20:01:30 2011
课程名称︰微积分甲上
课程性质︰必修
课程教师︰王金龙
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2010/10/21
考试时限（分钟）：30
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
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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