※ 引述《dreamenjoy (今天也很爽)》之铭言： : 1. : S is the region formed by x=y,x+y-3=0 and x=0.please find the : double integral of ∫∫(2x+2y-1)dxdy : 2. : The weekly cost to produce x widgets is given by : C(x)=75000+100x-0.03x^2+0.000004x^3, : 0<=x<=10000 and the demand function for the widgets is given by : p(x)=200-0.005x,0<=x<=10000 Assume that the company sells exascly what : they protuce. : (a)What are the marginal cost,marginal revenue and marginal profit when 2500 : widgets are sold? : (b)What are the marginal cost,marginal revenue and marginal profit when 7500 : widgets are sold? : 4. : 使用Lagrange求点(1.2.4)至平面2x-3y+z=4之最短距离 : 2 √4-y^2 √4-x^2-y^2 : 5.∫ ∫ ∫ z√x^2+y^2+z^2 dzdxdy : 0 0 0 x = (ρ)(cosθ)(sinψ) y = (ρ)(sinθ)(sinψ) z = (ρ)(cosψ) 则 |J| = (ρ^2)(sinψ) , 0 ≦ ρ ≦ 2 , 0 ≦ ψ ≦ π/2 , 0≦θ≦π/2 2 √(4-y^2) √(4 - x^2 - y^2) ∫ ∫ ∫ (z)(√(x^2 + y^2 + z^2)) dzdxdy 0 0 0 π/2 π/2 2 = ∫ ∫ ∫ (ρ)(cosψ)(ρ)(ρ^2)(sinψ) dρdψdθ 0 0 0 π/2 π/2 2 = ∫ ∫ ∫ (ρ^4)(sinψ)(cosψ) dρdψdθ 0 0 0 π/2 π/2 ρ^5 |ρ=2 = ∫ ∫ (------)(sinψ)(cosψ) | dψdθ 0 0 5 |ρ=0 π/2 π/2 32 = ∫ ∫ (----)(sinψ)(cosψ) dψdθ 0 0 5 π/2 16 |ψ=π/2 = ∫ (----)((sinψ)^2) | dθ 0 5 |ψ=0 π/2 16 = ∫ ---- dθ 0 5 16 |π/2 8π = (----)(θ)| = ----- 5 |0 5 : 6.Find dy/dx if x^y-y^x=0 : 麻烦各位了 感恩 -- 本周抽中:安 心 亚 本周最心碎:吴 怡 霈 本周最亮眼:王 薇 欣 动园木万社万医辛 麟六犁科大大忠复南东中国松机大剑路西港文内大公葫东南软园南展 物 栅芳区芳院亥 光张 技楼安孝兴京路山中山场直南 湖墘德湖湖园洲湖港体区港览 ○ ○○ ○ ○ ○◎ ○ ◎◎ ◎ ○ ○ ○◎ ○○○○○ ○◎○ ◎馆 王桦邵艾丝小桦张甯莎王欣李慧啾豆妹安亚吴霈廖娴小徐翊舒虎瑶可蜜儿蔓小刘萍 林玲 彩 庭莉 欣 钧 拉薇 怡 啾花 心 怡 书 娴裴 舒牙瑶乐雪 蔓蔓秀 志 --

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