中国数学考研 Graduate Math Exams

Math Online Tom Circle

中国”考研”究生:

考题难, 重视理论基础, 不是技巧。计算量大, 时间(3小时)不够。

国家 “及格” 底线 : 58~ 90分 (总分 : 150 分) – 根据 理工 / 经管系 , 不同重点大学, 底线各异。

http://www.bilibili.com/mobile/video/av2261356.html

[例子] $latex p (x) = a + bx+cx^{2}+dx^{3}$

$latex p(x) – tan x sim x^{3}, text { when } x to 0$

Find a, b, c, d ?

[Solution] :

1. Don’t use l’Hôpital Rule for $latex displaystyle lim frac {f}{g}$

2. Apply Taylor expansion :

$latex tan x = x + frac {1}{3}x^{3} + o (x^{3})$
$latex p (x) – tan x = a + (b -1)x + (c – frac {1}{3})x^{3} + o (x^{3})$

$latex p(x) – tan x sim x^{3}, text { when } x to 0 $

$latex iff boxed {a=0, b=1, c=frac {4}{3}}&fg=aa0000&s=2$

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