课程名称︰微积分乙下 课程性质︰ 课程教师︰王蔼农 开课学院： 开课系所︰ 考试日期（年月日）︰96/06/17 考试时限（分钟）：110分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 4xy 1. f(x,y) = ─────── Find max, min, and saddle points (5/50) (x^2+1)(y^2+1) 2. (x,y) = (-2,0) , (0,1) , (2,3) Find the least squares regression line y = mx+b = ? (5/50) 3. Find the highest point of the circle x^2+y^2+z^2 = 6 , 2x+y-z = 2 (5/50) 4. u = u(x,y) x = rcosθ , y = rsinθ , second partial derivative (用 σ 代表偏微符号) σ^2 u σ^2 u σ^2 u σ^2 u σu σu ─── = ? ─── + ? ─── + ? ─── + ? ─── + ? ─── (5/50) σy^2 σr^2 σrσθ σθ^2 σr σθ 3 x (9-x^2) ? ? ? 5. ∫∫∫ f(x,y,z) dzdydx = ∫∫∫ f(x,y,z) dxdzdy (5/50) 0 0 0 ? ? ? 6. ∫∫ (x+y)^2‧sin^2(x-y) d△ = ? R is the region of a square with R (5/50) vetices (0,1) (1,2) (2,1) (1,0) _______ 7. Find the surface area. Z=√(1-y^2) , 0≦x≦y≦1 (5/50) → x → y → → → → 8. F = ─── i + ─── + j + k , r = (x,y,z) , dr = (dx,dy,dz) x^2+y^2 x^2+y^2 q → → p = (1,2,3) , q = (4,5,6) , ∫ F‧dr = ? (5/50) p ydx - xdy 9. ∫ ────── = ? C is the segment from (1,1) to (2√3,2) (5/50) C x^2 + y^2 → → → → 10. F = 2yi + 3zj + xk C is the triangle (0,0,0) (0,2,0) (1,1,1) → → ∫ F‧dr = ? (5/50) C --

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