→ Pineapple225:你也太快了吧= =+ 我剛打好的說OTL 11/09 10:07
課程名稱︰微積分甲
課程性質︰數學 - 微積分
課程教師︰周青松
開課學院：(下面有限定)
開課系所︰生機、生工、地質、地理、工管等
考試年月日︰2007/11/9 星期五
考試時限（分鐘）：8:10---10:00 遲到20分鐘不得進場
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Ⅰ. Give necessary and sufficient conditions on A and B for the function
｛Ax-B , x≦1
f(x) =｛3x , 1＜x＜2
｛Bx^2-A , 2≦x
to be continuous at x=1 but discontinuous at x=2.
Ⅱ.Show that
sin x
lim ─── = 1
x→0 x
1-cos x
and lim ──── = 0
x→0 x
Ⅲ. Find A and B given that the function
f(x) =｛x^3 , x≦1
｛Ax+B , x＞1
is differentiable at x=1.
Ⅳ. find A and B given that the that derivative of
f(x) =｛Ax^3+Bx+2 ， x≦2
｛Bx^2+A , x＞2
is everywhere continuous
Ⅴ a. find the critical points ot the function
f(x)=(x^3-1.5x^2-6x+2)/4 , x屬於[-2,無限)
to chassify all the exreme values and sketch the graph
b.find d given that (d,f(d)) is a point of inflection of
the graph of
f(x)=(x-a)(x-b)(x-c)
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◆ From: 140.112.7.59
※ 編輯: uhks 來自: 140.112.7.59 (11/09 09:26)