課程名稱︰微積分甲上
課程性質︰大一共同必修
課程教師︰張志中
開課學院：工學院
開課系所︰數學系
考試日期（年月日）︰ October 21,2008
考試時限（分鐘）：一節課
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Evaluate the following limits, if it exists. If the limit does not exist,
explain why.
(a) (10 points) t^2-9
lim ──────
t→-3 2t^2+7t+3
(b) (10 points)
x^2-1
lim ────
x→1 │x-1│
2.Evaluate f'(1) of the following functions.
(a) (10 points)
f(x)= (x(x-2)(x^2+1)^(-1))^(1/3) 題目是用分式寫
(b) (10 points)
f(x)=arcsin(√2x/2)
3.
f(x)={ x^3sin(1/x) ,when x≠0
0 ,when x=0
(a) (10 points) Does lim x→0 f(x) exist? If so, what is it? If NOT ,why not?
(b) (10 points) Is f(x) differentiable at x=0? If so, explain your reason and
compute f'(0) If NOT, why not?
4.f(x)={ x+b , when x<0
cosx-b, when x>=0
(a) (10 points) Does there exist a number b such that f(x) is continuous
at x=0?
(b) (10 points) Does there exist a number b such that f(x) is differential
at x=0? Give reason for your answers.
5.(20 points) Show that : If (Xo,Yo) is a point on the graph of 2 2
X Y
──+──=1
a^2 b^2
, then the tangent line which passes through (Xo,Yo) is
Xo*X Yo*Y
───+─── = 1 .
a^2 b^2
※ 編輯: chihyanglee 來自: 140.112.233.26 (10/28 22:08)