作者novem3000 (3000)
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标题[试题] 98暑修 周青松 微积分甲上 1st考试
时间Thu Jul 8 11:25:52 2010
课程名称︰微积分甲上
课程性质︰暑修
课程教师︰周青松
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2010/7/8
考试时限（分钟）：50分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
It's necessary to explain all the reasons in detail and show all of your
work on the answer sheet. Or you will NOT get any credits.If you used any
theorems in textbook or proved in class, state it carefully and explicitly.
1. Decide whether ot not the limit lim f(x) exists, where
x→3
{ x^2 , x＜3
f(x) ＝ { 7 , x＝3
{ 2x + 3 , x＞3
{ 2x^2 - 1 , x＜2
2. Set f(x) ＝ { A , x＝2
{ x^3 - 2Bx , x＞2
For what values of A and B is f continuous at 2.
3. Find f'(c) if it exists, where c＝3 and f(x) ＝ { -x^2 / 2 , x＜3
{ -3x , x≧3
4. Find A and B given that the derivative of
f(x) ＝ { Ax^2 + B , x＜-1 is everywhere continuous.
{ Bx^5 + Ax + 4 , x≧-1
5. Find a function y ＝ f(x) with the given derivative
y'＝ 3(x^2 + 1)^2 (2x).
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