作者assignment (凝愿)
看板NTUBA00study
标题[转录][试题] 周青松 微积分甲 93上期中
时间Mon Oct 22 22:08:30 2007
※ [本文转录自 NTUBA00 看板]
作者: assignment (凝愿) 看板: NTUBA00
标题: [转录][试题] 周青松 微积分甲 93上期中
时间: Sun Oct 21 21:21:41 2007
※ [本文转录自 NTU-Exam 看板]
作者: backslide ( 呀~~~~~) 看板: NTU-Exam
标题: [试题] 周青松 微积分甲 93上期中
时间: Sun Nov 14 10:38:14 2004
课程名称︰微积分甲
课程性质︰共同必修
课程教师︰周青松
开课系所︰
考试时间︰2004.11.8
试题 :
Ⅰ. Give necessary and sufficient conditions on A and B for the function
｛Ax-B , x≦1
f(x) =｛3x , 1＜x＜2
｛Bx^2-A , 2≦x
to be continuous at x=1 but discontinuous at x=2.
Ⅱ. a. Find A and B given that the function
f(x) =｛x^3 , x≦1
｛Ax+B , x＞1
is differentiable at x=1.
b. Find f'(1) given that f(x)=｛^2 , x≦1
｛2x-1 , x＞1 .
Ⅲ. Let f and g be differentiable functions such that f'(x)=g(x) and
g'(x)=f(x), and let H(x)=[f(x)]^2-[g(x)]^2.
Find H'(x).
Ⅳ. Let f be differentiable on an open interval O. Such that
(i) if f'(x)＞0 for all x in O, then f increases on O.
(ii) if f'(x)＜0 for all x in O, then f decreases on O.
Ⅴ. Find the critical numbers, the points of infletion (of any), claesify all
the extreme values, of the function f(x)=1/4[x^3-(3/2)x^2-6x+2],x{-2,∞].
Sketch the graph.
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