課程名稱︰微積分甲上
課程性質︰必修
課程教師︰朱樺
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2013.10.14
考試時限（分鐘）：60
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(20%)Find the limit.
(a) [x]-2
lim --------
x→-2+ [x^2]-4
(b) [x]-x
lim ------------
x→-2- [x^2]-x^2
(c)
lim (2^x+3^x+4^x)^(1/x)
x→∞
(d)
lim (2^x+3^x+4^x)^(1/x)
x→-∞ ＿＿＿＿
√9x^2+1
2.(10%) Find all asymptotes of the curve y=------------
x-4
3.(10%) Let f(x) be a continuous function which map the interval [2,3] into
[8,10]. Show that there exists c∈[2,3] such that f(c)=2c+4
x^2sin(1/x) x<0
4.(20%)Let f(x)={ a x=0
logx(b) x>0,x≠１
(a)Find all numbers a and b such that f(x) is continuous in its domain.
(b)Find all numbers a and b xuch that f(x) is differentiable in its domain.
t
(hint:lim -----=∞)
t→∞ lnt
5.(10%)Differetiate the function f(x)=sin^2(tan(x^3)cos(4^x))
6.(15%)Find akk normal lines of y=x^2 which pass through the point (2,4).
1
7.(10%)Let y=------- .Find y^(n)
x^3-x
8.(15%)If x+xy+y^2=1, find the value of y^m at the points where x=0.
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.112.249.103
※ 文章網址: http://www.ptt.cc/bbs/NTU-Exam/M.1404153009.A.FD7.html