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.... http://www.wretch.cc/album/show.php?i=jane050177&b=6&f=1173614532&p=0 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 = = 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?? 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) ??) 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)