課程名稱︰微積分乙
課程性質︰必修
課程教師︰李聰成教授
開課學院：管院
開課系所︰管院
考試日期（年月日）︰2009/11/12
考試時限（分鐘）：2小時40分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
請將每一步驟表達清楚 ,不可以只寫答案
1. Is there a number a such that
lim 3x^2+ax+a+3
------------------
x->-2 x^2+x-2
exsits? If so, find the value of a and the value of the
limit.
2.Evaluate the lim it.
lim √(9x^6-x)
x->-∞ --------------
x^3+1
3.Evaluate the limit.
lim (16+h)^1/4 -2
h->0 -------------------
h
4.Sketch the graph of the given function , making use
of any sutiable information you can obtain from the
function and its first and secong derivatives.
x^3
f(x) = ------------
x^2 +1
5.Find all points on the graph of the function
f(x)=2sinx +sin^2(x)
at which the tangernt line (切線) is horizontal (水平)
6.Use implicit differentiation to find an equation of the
tagent line to the curve
x^3+y^3 =6xy
at the point (3,3)
7.Let f(x)= (√x+c^2 )-c/x ,where c>0 is a real constant.
(a) What is the domain (定義域) of f .
(b) How can you define f at x=0 in order for f to
be continuous there?
8. Show that the function
f(x) = x^2sin(1/x) , if x≠0
0 , if x=0
is differentiable on (-∞ , +∞ ) and find f' .
9.Two cars moving from the same point . One travels sounth
at 30 km/h and other travels west at 72 km/h .
At what rate is the distance between the cars increasing two hours
later?
10.Find the points on the ellipse(橢圓)
4x^2 +y^2 =4
that are closet (最近) to and farthest (最遠) away
from the point (1,0) .
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.231.101.193