作者Thitta (胖胖 )
看板NTUIB99
标题[转录][考古题] 94上 张秀瑜 微积分乙 期中
时间Sat Nov 11 20:03:35 2006
※ [本文转录自 NTU-Exam 看板]
作者: diep (隐藏人物) 看板: NTU-Exam
标题: [试题] 94上 张秀瑜 微积分乙 期中
时间: Sun Nov 13 16:11:17 2005
课程名称︰微积分乙上
课程性质︰共同必修
课程教师︰张秀瑜
开课系所︰管院、地理、经济
考试时间︰94/11/10
试题 :
1. ___
(a) Find lim√x+1 -2/(x-3).
x→3
应该是1/4
(b) Prove that lim x^2cos(1/x^2) = 0.
x→0
用夹击定理，课本88页
(c) Find all values of a such that f is continuous on R, where
{ x^2, if x > a;
f(x) = {
{ x+1, if x≦ a.
2
作x =x+1﹝是这样吗？﹞
(d) Give a short explanation of why the following approximation is valid.
____
√4.02 ≒ 2 + 1/4(0.02)
这啥？
2.Show that the function g(x)= x∣x∣has an inflection point at (0,0), but
g"(0) does not exist.
dy 3 _
3.Find —. (a) y = 2csc (√x) (b) tan(x/y) = x+y
dx
chain rule 答案好长...不会打...= =
4.If y = f(u) and u = g(x), where f and g are third differentiable function,
d^2y d^2y (du)2 dy d^2u d^3y
— = — (－) + — — . Find a formula for — similar to
dx^2 du^2 (dx) du dx^2 dx^3
the one given above.
这题是课本197页的第65题，老师最近一次上课有讲过，有背有保佑
5.Prove that if a > 0 and n is any positive integer, then the polynomial
function
2n+1
p(x) = x + ax + b
cannot have two real roots.
......
6.Find an equation of the line through the point (3,5) that cuts the least
area from the first quadrant.
有人会这题吗...
7.Sketch the graph of y = x^3 －1/x^3 + 1
事实证明，真的会考画图题，详情请见第四章
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◆ From: 140.112.240.101
1F：→ Thitta:祝大家顺利...= = 11/11 20:15
※ 编辑: Thitta 来自: 140.112.240.101 (11/11 20:32)
※ 编辑: Thitta 来自: 140.112.240.101 (11/11 20:33)
2F：推 christless:这不推还是人吗???旭峰乾爹~ 11/11 20:38
※ 编辑: Thitta 来自: 140.112.240.101 (11/11 21:36)
※ 编辑: Thitta 来自: 140.112.240.101 (11/11 22:19)
3F：推 littlecutie:推一个好了 11/11 23:09
※ 编辑: Thitta 来自: 140.112.240.101 (11/12 00:03)
4F：推 troysky:大推~ 11/12 10:03
5F：→ nickivan:(d)Let f(x)=x^(1/2),since f(x+dx)=f(x)+f'(x+dx)+..... 11/12 13:26
6F：→ nickivan:hence (4.02)^(1/2)=f(4+0.02)=f(x=4)+f'(x=4)(0.02)+... 11/12 13:30
7F：→ nickivan:=4^(1/2)+1/2(4)^(-1/2)(0.02)+.....~2+1/4(0.02) 得证 11/12 13:33
8F：→ nickivan:(c)答案不是 1吧？画图可以看出来喔～a有两个值 11/12 13:47
9F：推 littlecutie:来偷写一下好了 11/12 21:52
10F：推 littlecutie:感觉助教颇威 11/12 21:52
11F：推 Thitta:还没细看，先推一个好了，感谢~~~ 11/12 21:58
12F：推 littlecutie:决定先看电视！！！ 11/12 22:02
13F：推 Thitta:突然发现x^2好像是X平方的意思，我一直以为是乘号 11/12 22:15
※ 编辑: Thitta 来自: 140.112.240.101 (11/12 22:21)