※ 引述《sky2857 (楷中)》之銘言：
: ※ [本文轉錄自 NTU-Exam 看板 #18oeEZE8 ]
: 作者: Julibea (Julia) 看板: NTU-Exam
: 標題: [試題] 96暑 周青松 微積分甲下期末考
: 時間: Fri Sep 12 22:58:42 2008
: 課程名稱︰微積分甲下(暑修)
: 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）︰2008/09/09
: 考試時限（分鐘）：120分鐘 (8:10~10:10)
: 是否需發放獎勵金：yes, thanks
: 試題 :
: I. A) Find F(t) given that F'(t)= 2cost i - t(sint^2) j + 2t k
: F (0)= i + 3 k
: B) Show that, if γis differentiable vector funtion of t,
: where r =∥γ∥> 0,
: d γ 1 dγ
: then ── (──) = ── [(γ x ──) x γ]
: dt r r^3 dt
: II. Let γ= x i + y j + z k and r =∥γ∥> 0
: A) Prove that, for each interger n, ▽r^n = nr^(n-2)γ
以上好無聊
: B) Find ▽(e^r)
這好像要算一下吧
e^r * γ/r吧
: III. A) Find the directional derivative of the function
: f(x,y,z)= 2x(z^2) cosπy
: at the point P(1,2,-1) toward the point Q(2,1,3)
: B) Use the chain rule to find the rate of change of
: f(x,y,z)= (x^2)y + zcosx
: with respect to t along the twisted curve
: γ(t)= t i + t^2 j + t^3 k
好煩XD
: IV. A) Use double integration to calculate the area of the region
: Ω enclosed by y=x^2 and x+y=2
9/2嗎? = =
: 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.
ab^2 pi
: V. A) Find the mass of a solid riht circular cylinder of radius r
: and height h given that the mass density varies directly
: with distance from the lower base.
圓筒
密度應該是 kz吧
然後就開始積分了
1/2 k h^2 再乘上圓面積吧
所以 1/2 k h^2 pi r^2
: B) Evaluate the triple integral
: ∫∫∫ 2ye^x dxdydz , where T is the solid given by
: T
: 0≦y≦1, 0≦x≦y, 0≦z≦x+y
重複
: (每大題均20分)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.4.202