→ ss355227:這篇感覺比較多非習題的部分 應該 不會考吧= =? 05/14 15:02
※ 編輯: ss355227 來自: 140.112.7.214 (05/14 15:14)
推 steve1012:是習題不過是後面的 05/14 15:28
※ [本文轉錄自 NTU-Exam 看板 #1AdpwufY ]
作者: iwantowaylaw (我要成為太鼓達人) 看板: NTU-Exam
標題: [試題]
時間: Thu Sep 3 11:57:43 2009
課程名稱︰ 暑修微積分甲下第二次期中考
課程性質︰
課程教師︰ 周青松
開課學院：
開課系所︰
考試日期（年月日）︰2009/9/3
考試時限（分鐘）：2小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）
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題目中好像有些筆誤
我先不改喔 大家應該知道~
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試題 :
Make sure to give sufficient reason in each problem or you will NOT get any
credit for your answer.
A.
(a)
Set a = a1i + a2j + a3k
and b = b1i + b2j + b3k
Show that a x b = (a2b3-a3b2)-i(a1b3-a3b1)j+(a1b2-a2b1)k
無言不知道要證啥
(b)
Set a = a1i + a2j + a3k
b = b1i + b2j + b3k
c = c1i + c2j + c3k
| a1 a2 a3 |
Show that (a x b) ‧ c = | b1 b2 b3 |
| c1 c2 c3 |
p.668 Example 3
B.
(a)Find f(t) given that f'(t) = 2costi-tsint^2+2tk and f(0)=i+3k
應該不難吧 我算 f(t) = 2sint + 1 i + 1/2 cost^2 -1/2 j + t^2 +3 k
(b)Find f(t) given that f'(t) = ti-t(1+t^2)^(-1/2)+te^tk and f(0)=i+2j+3k
重複
C.
(a)
Show that if γ is a differentiable vector function of t ,then the function
r = ║γ║ is differentiable at where it is not zero and
dγ dr
γ‧ ── = r ──
dt dt
p.703 (14.2.3) 證明在p.704上方
(b)
Show that for each integer n and all γ≠0 we have ▽r^n = nr^(n-2)γ
未知
D.
(xy)^2
Set g(x,y) = ─── if (x,y) ≠ (0,0)
x^4+y^4
0 if (x,y) = (0,0)
dg dg
(a)Show that ─(0,0) and ─(0,0) both exist and evaluate their values
dx dy
(b)Show that lim g(x,y) doesn't exist
(x,y)→(0,0)
p.785 第29題 要練習過吧
E.
(a)
Find all function with gradient yzi + (xz+2yz)j + (xy+y^2)k
未知
(b)
2xy
Set f(x,y) = ─── if (x,y) ≠ (0,0)
x^2+y^2
0 if (x,y) = (0,0)
Show that f is not differentiable at (0,0)
應該是從不同方向逼近原點的值不同 所以不連續 所以不能微分吧!?
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感覺這篇過多非習題題目......
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