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标题[转录][试题] 95上 周青松 微积分甲 期中考试试题
时间Mon Nov 13 21:19:24 2006
※ [本文转录自 NTU-Exam 看板]
作者: Jerrynet (Jerry) 看板: NTU-Exam
标题: [试题] 95学年度上学期 周青松 微积分甲 期中考试 试题
时间: Mon Nov 13 18:29:39 2006
课程名称︰微积分甲
课程性质︰数学 - 微积分
课程教师︰周青松
开课学院：(下面有限定)
开课系所︰生机、生工、地质、地理、工管等
考试时间︰2006/11/13 星期一
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
I
A) Determine the discontinuities, if any, of the following function:
{ 2x+1 , x <= 0
f(x) = { 1 , 0 < x <= 1
{ x^2+1 , x > 1
B) Give necessary and suffcient condition 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) Given that f(x) = { x^2 , x <= 1 find f'(1)
{ 2x-1 , X > 1
B) Find A and B given that the function :
f(x) = { x^2-2 , x <= 2
{ Bx^2+Ax, x > 2
is differentiable at x=2
III
Find the indicated derivative.
A) d/dt[ t‧d/dt(cos(t^2)) ] B) d/dx[ sin(f(3x)) ]
IV
Let f(x) = (sec(x))^2 and g(x) = (tan(x))^2
on the interval O = (-π/2 , π/2)
A) Show that f'(x) = g'(x) for all x 属於 O
B) The result in part A) implies that f - g = C, a constant, on O.
Find the value of C
V
Sketch the graph of the function f(x) = 1/4‧x^4 - 2(x^2) + 7/4
for x 属於 [-3 , 3]
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