[轉錄][試題] 98下周青松微積分甲下期末考

看板NTUBIME103HW作者sky2857 (楷中)時間14年前 (2011/06/16 00:30)推噓5(5推 0噓 0→)

留言5則, 5人參與討論串1/3 (看更多)

※ [本文轉錄自 NTU-Exam 看板 #1CD0FJ03 ] 作者: SWW (鼠嗚嗚) 看板: NTU-Exam 標題: [試題] 98下周青松微積分甲下期末考時間: Wed Jul 7 12:34:24 2010 課程名稱︰微積分甲下課程性質︰必修課程教師︰周青松開課學院：理學院開課系所︰考試日期（年月日）︰2010/6/21 考試時限（分鐘）：100分鐘是否需發放獎勵金：是（如未明確表示，則不予發放）試題 : A.(a) Findｆwith the conditionｆ'(t)=2ｆ(t) and ｆ(0)=i-k. (b) Letｆbe a differentiable vector-valued function. Show that whenver ∥ｆ(t)∥≠0. d ｆ'(t) ｆ(t)‧ｆ'(t) —(————— － ————————ｆ(t) dt ∥ｆ(t)∥ ∥ｆ(t)∥^3 B.(a) Find the directional derivative of f(x,y,z)=Ax^2 + Bxyz+ Cy^2 at the point P(1,2,1) in the direction of Ai+Bj+Ck. (b) Assume that ▽f(x) exists. Prove that, for each integer n, n n-1 ▽f (x)=nf (x)▽f(x). Dose the result hold of n is replaced by an arbitary real number? C.(a) Use the chain rule to find the rate of change of f(x,y,z)=x^2 y+zcosx with repect to t along the twisted cubic ｒ(t)=ti+t^2 j+t^3 k. (b) Set r=∥ｒ∥, whereｒ=xi+yj+zk. If f is a continuously differentiable function of r, then ｒ ▽〔f(r)〕=f'(r)—, where r≠0 　　　　　 r D.(a) Evaluate the double intergral __ ∫∫ √xy dxdy, Ω:0≦y≦1, y^2≦x≦y. Ω (b) Calculate the volume within the cylinder x^2 + y^2 = b^2 between the planes y+z=a and z=0 given that a≧b＞0. E.(a) Evaluate π/2 π/2 1 ∫ ∫ ∫e^z cosxsiny dzdydx 0 0 0 (b) Evaluate the triple integral ∫∫∫2ye^x dxdydz, T where T is the solid given by 0≦y≦1, 0≦x≦y, 0≦z≦x+y. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.167.130.132 ※ SWW:轉錄至看板 b982040XX 07/07 12:35 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 223.137.230.120

推

andrew801222

06/16 00:35, , 1^F

06/16 00:35, 1^F

推

kn930121

06/16 00:38, , 2^F

06/16 00:38, 2^F

推

btf2

06/16 01:14, , 3^F

06/16 01:14, 3^F