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數學與統計 大學

第五題不太懂 求解

上午7:21 0 2. | 66 I') x ' A - WA -- 2x +3 (2) g(x)=(42-7) 則 g(2)=? (3) 設 h(x)= 則 h'(3)=? 2x3) 3x-8 (4)g(x)=2tan(x)+(sin(x2 + 2x)) g'(0)=? 2 設某商品之需求函數為 x=12000-10p° 其中x表示需求量p 表示 價格試計? (a). 需求彈性 E(10) (b). E(20)並解釋其意義(C). E(30)並解釋其意義 (d). 當p=16 時 p上升1%,此時收益會增加或減少?為何? 3. 設硬碟製造商 Texar,欲以每台p元的批發價每周在市場上供應x千台 1GB UBS 碟機x 與p的關係為供應方程式 x=-3xp+p°=0 目前每台硬碟的單價為10 元供 量為4000 台且單價以每周 0.1 元的速率上漲,則供應量的變化率為何? 4.設函数f(x)=f(x); x2 x2 +9 試計算f之 (1) 臨界點 (2). 遞增區間遞減區間 (3).反曲點 (4). 凹口向上區間,凹口向下區 (5) 相對極大值或相對極小值 (6).漸進線 (7) 圖形 5. (a). g(x)=2x5.e-(x-1) „W! g'(1)= ? (b). h(x)=x3 . log. 12x-1) 則 h(1)=? (c). m(x)=6* x3 – 5* x2 , m'(1)= ? (d).L(x)=x2* BIJ L'(1)=? 6. 設某公司生產一款電動鉛筆機之每天邊際成本為 C'(x)=0.006x2-0.06x+2 其中C'(x)是以元/個計之,而x表產量, 此外該公司每天固定成本為100 元, 試計算下列: (a). 生產前30 個 產品之每天的總成本 (b). 生產第31 個產品時之每天的總成本 7. (a). F(x)=cos(3x - 2x+5) F(0)=? (b).設一長為10 英呎的梯子傾斜靠在一垂直 牆上,已知梯腳以1/4(英呎/分鐘)速度向右滑動(遠離牆面),則梯腳離牆8英呎時样 沿牆向下滑動的速度為何?(c).試用微分之線性近似的概念,求:16.08近似值至 數點第4位。(需寫出計算過程)。 8. 試計算下列: 第一頁 共2頁 x2 =? (a) lim x-00%-2- (b). lim ((In(n)) n2 =? (c). lim (1) n00 9. (a). 試以微積分之方法求出內接於半徑為9之半圓內之長方形的最大面積, (b) 試計算點(14) 至曲線 y= 2x 之最近的距離 | 立

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數學與統計 大學

大一公衛系微積分,求第二題解

公衛系 微積分期末考 (28/12/2018) 1. Use the Laplace transform to solve the differential equations. (1) j(t)+2y(t) = x(t), y(0)=1, x(t)=10, t20 (20) (2) Intravenous glucose is a treatment. Disposed at a fixed rate k grams per minute inputs into the blood, while blood glucose will be converted to other substances or moved to another place, at a rate proportional to the amount of glucose in the blood, the proportionality constant is a (a> 0), the initial amount of glucose in the blood is M. A. Find the variation in the amount of glucose in the blood (15) B. Determining the equilibrium, the amount of glucose in the blood. (5) = 2. SI Epidemic Model : The size of the population, n+1, remains fixed. Let i(t) be the number of infectives at time t, and let s(t) be the number of individuals who are susceptible. Given an initial number of infectives iO), we would like to know what will happen to i(t). SI Epidemic Model is described by the differential equation. di(t) = k·i(t).s(t) ......(5.1) dt i(t)+s(t)=n+1 i(0)=i, (1) Solve this differential equation of the SI Epidemic Model (5.1). (10 h) (2) What is the peak times t of the epidemic spread? (10) 3. Consider the Two-compartment physiological models and is shown in figure 1. C1 (t) represent the drug concentration in the first compartment and C2 (t) represents the drug concentration in the second compartment. Vi and V2 represent the compartment volume. Use the first order linear differential equation general solution to solve the C1 (t) (20 ) and use the Laplace transform to solve C2 (t). 【20 分). | 世」!()

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