[試題] 93下漢水期末考 (附詳解)
一 Let D be the surface x^2 + 4y^2 + 4z^2 = 16 and the temperature at the
point (x,y,z) on D is T(x,y,z) = 8y^2 + 4xy - 16z + 400. Find the higest
and lowest temperatures on the surface. (20%)
4 1 2 2cos(x^2) ꄊ二 Find the integral ∫{∫ [∫ ────── dx] dy}dz (15%)
1 ꈠ0 2y √z ꌊ
三 Let D be a thin plate outside the circle r = 5 and inside the circle
r = 10cosθ. Suppose the density at the point (x,y) is den(x,y) = 1/r .
Find the mass of D. (15%)
四 Let D be region bounded by the cylinder x^2 + y^2 = 9 and the planes z = 0
, y + z = 6. Suppose the density at the point (x,y,z) on D is
den(x,y,z) = 2z. (20%)
(1) Find the mass of D.
(2) Find the center of mass of D.
→ → → →
五 Let F (x,y,z) = 2z i + 3x j + 5y k and S be the surface in the outward
→ → → →
direction r (r,θ) = (rcosθ) i + (rsinθ) j + (9-r^2) k , 0≦ r ≦3,
→ →
0≦θ≦2π. Find ∫∫▽ ×F ‧n dσ. (15%)
s
→ → → →
六 Let F (x,y,z) = 0 i + 0 j + (7z-2) k and Let D ={(x,y)│x^2 + y^2 ≦9}.
Suppose f(x,y)≧0 for any (x,y)εD and
K ={(x,y,z)│x^2 + y^2 ≦9, 0≦ z ≦f(x,y)} If the volume of K is 70,
→ →
find the flux ∫∫F‧n dσ. (15%)
s
我不知道算的對不對 不過反正PO上來大家一起檢討比較快...
有錯請跟我說 歡迎推文或回文
另外 我應該都會在MSN上 想罵我為什麼算的那麼爛也歡迎!!!
我估計我計算錯誤會很多 請大家不要在意....
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http://www.wretch.cc/album/show.php?i=jane050177&b=6&f=1173614533&p=1
http://www.wretch.cc/album/show.php?i=jane050177&b=6&f=1173614534&p=2
如果圖片很模糊 可以另存新檔從電腦上打開來放大比較快......
我的第一題算的λ很醜 大家也是算的這樣子嗎??
然後我第五題不會算 請救救我 = =
推
06/14 16:01, , 1F
06/14 16:01, 1F
→
06/14 16:08, , 2F
06/14 16:08, 2F
推
06/14 16:13, , 3F
06/14 16:13, 3F
→
06/14 16:14, , 4F
06/14 16:14, 4F
→
06/14 16:15, , 5F
06/14 16:15, 5F
推
06/14 18:36, , 6F
06/14 18:36, 6F
所以第一題的答案是什麼呢??
然後第二題我還是算 3sin4耶 可以跟我講我錯在哪嗎??
→
06/14 18:38, , 7F
06/14 18:38, 7F
對不起我第三題錯了 的確角度應該是從pi/3~-pi/3
答案應該是10(√3-π/3) ??)
推
06/14 20:41, , 8F
06/14 20:41, 8F
→
06/14 20:42, , 9F
06/14 20:42, 9F
→
06/14 20:42, , 10F
06/14 20:42, 10F
→
06/14 20:42, , 11F
06/14 20:42, 11F
謝謝華均葛格ˇ
第三題更正答案為10(√3-π/3) 第二題更正為sin4
※ 編輯: jane050177 來自: 123.193.230.78 (06/14 20:54)