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」!()

求解第22題 算出0.1587跟0.8416之後不知道怎麼算

190 BASIC STATISTICS 基礎統計學 O 21. 設某人由公司返家的時間為近常態分配,平均數為24分,標準差為3.8分。試問某人 返家3次中有2次至少超過半小時之機率為何? 22. 設某一工廠所生產之零件其長度呈常態分配,已知平均數為0.5时,標準差為0.05 。 零件之長度在0.45~0.55 时之間為合格,問此工廠之產品為不合格品的機率為何? 23. 設某產品平均有4%不合規格,今檢查 800件,試求少於35件不合格的機率。 (提示:先寫出二項分配的式子,並以常態分配近似之。) O 24. 假設有23%患有高血壓的病人服用某一藥物會產生不良影響,試利用常態分配求出120位 高血壓病患服此藥物之後,超過32位產生不良影響的機率。 25. 假設某大學有30%學生使用Line Pay,今從該校隨機抽取 200名學生,試問其中有50~10 人使用 Line Pay的機率為何? 1 9 26. 設有兩個獨立的隨機變數X、Y,令W = X+Y,試依以下不同的分配: (1) X ~B(10, 0.4), Y~(20, 0.4) (2) X~N(15, 3), Y~N(10, 7) ***: (a) E(W); (b) Var(W): (c) P(W = 5); (d) E(W + 3) ; (e) Var(2W + 3) º ( 27. 假設大學生每天玩手遊的時間呈常態分配,每天玩的時間少於3小時占33%;超過8小時, 占5%,試求大學生每天玩手遊的平均時間。 , 0 二主|| '--- 1主日已的

求解21,22,38🙇 section1.3不用理他 equation 2.1.5是微分的定義式

Z (b) Use the acceleration curve from par (a) to estimate the 10 seconds. What are the units for jerk? 45) The lel defined ||||| V has a vertical tangent line at (0,0). and jerk at = 38, Let f(x) = V. x ( (a) If a 40. use Equation 2.1.5 to find s'a). (b) Show that f'(o) does not exist. (c) Show that y- (Recall the shape of the graph of f. See Figure 1.2.13.) 39. (a) If g(x) = x?, show that g'(0) does not exist. (b) Ifa * 0, find g'(a). (c) Show that y = x2 has a vertical tangent line at (0,0). c (d) Illustrate part (c) by graphing y - x2) if the sided (a) F | 40. Show that the function f(x) = |x - 6 is not differentiable at 6. Find a formula for and sketch its graph. (b) Where is the greatest integer function () = [x] not

求解21,22,38🙇 section1.3不用理他 equation 2.1.5是微分的定義式

(d) Use the definition of derivative to prove that your guess in part (c) is correct. 14-21 Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. 14. f(x) = 3x - 8 15) f(x) = mx + b 16. f(x) - 4 + 8x - 5x? (17) f(x) = x - 3x + 5 18. f(x) - x + V g(x) - 19- x? - 1 20. f(x) 21s(x) x2 2.x - 3 (hours) arger. The graph hat the battery purs). (r)? graph - a 22.) a) Sketch the graph of f(x) - V6 - x by starting with the graph of y # and using the transformations of Section 1.3. (b) Use the graph from part (a) to sketch the graph of f! (c) Use the definition of a derivative to find f'(x). What are the domains of f and f'? (d) Use a graphing device to graph f' and compare with your sketch in part (b). lo-TE 23. (a) If f(x) = x + 1/x, find f'(x). (b) Check to see that your answer to part (a) is reasonable by JE comparing the graphs of f and f'. 1 (hours) shows how 24. The table given tho hai

請問e小題怎麼算，謝謝🙏

a POPULATION GROWTH It is estimated that 1 years from now, the population of a certain 6 suburban community will be P(1) = 20 - t + 1 thousand inst . a. Derive a formula for the rate at which the population will be changing with respect to time t years from now. b. At what rate will the population be growing 1 year from now? c. By how much will the population actually increase during the second year? d. At what rate will the population be growing 9 years from now? e. What will happen to the rate of population growth in the long run?

求解21,22,38🙇 section1.3不用理他 equation 2.1.5是微分的定義式

(d) Use the definition of derivative to prove that your guess in part (c) is correct. 14-21 Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. 14. f(x) = 3x - 8 15) f(x) = mx + b 16. f(x) - 4 + 8x - 5x? (17) f(x) = x - 3x + 5 18. f(x) - x + V g(x) - 19- x? - 1 20. f(x) 21s(x) x2 2.x - 3 (hours) arger. The graph hat the battery purs). (r)? graph - a 22.) a) Sketch the graph of f(x) - V6 - x by starting with the graph of y # and using the transformations of Section 1.3. (b) Use the graph from part (a) to sketch the graph of f! (c) Use the definition of a derivative to find f'(x). What are the domains of f and f'? (d) Use a graphing device to graph f' and compare with your sketch in part (b). lo-TE 23. (a) If f(x) = x + 1/x, find f'(x). (b) Check to see that your answer to part (a) is reasonable by JE comparing the graphs of f and f'. 1 (hours) shows how 24. The table given tho hai

求第17題

人 14. Profit The profit 16. 人2/ 2 / Wcd/e Figure for 17 Figure for 18 18. 95 。Volume_AIl edgaes of a cube Pro hom selling x units Of a product ls glven by 2三 510N 0 atarate ot 9 units per dl the prottt when (am) 、 二 4 The sales are Jncreasing ay. Find the rate Of change Of 00 units and (bD)文三 600 unjts, qre expanding at a rate How fast is the volume changing when each edge is (a) 2 centimeters and (b) 10 centimeters? ot 6 centimeters per second, Surface Area_AI edges ofacube are expanding at a Tate of 6 centimeters Per Second. How fast is the surface area changing when each edge is (a) 2 centimeters and (b) 10 centimeters? 。 Boating_A boat is pulled by a winch on a dock, and te winch is 3 meters above the deck of the boat (See figure). The winch pulls_the Tope at arate of 1 meter per second. Find thexspeed 6fthe boat when 5 meters 9t Tope 1S out. What happens to the Speed of the boat as it gets closer and closer to the dock? Shadow Length “Aman 2meters tall walks at arate 0f ].5 meters per second away from a light that is 5 meters aboye the ground (see figure). | (a) When he js 3 meters from the base of the light, at 人 和 生0) what rate js the tip of his shadow moving。 (b) When he js 3 meters from the base of the at what rate js the Jength of his shadow changlng。 Air Traffic_Control An airplane flying at an altitude Of 10 kilometers pasSes directly over aradar 蟬戰品 品 figure). When the airplane is 26 kilometerS away ($ 三 26), 由 卅0 ee 21, 22 23 24 12 店

求解64題。統計間斷分配

下 “64. Recent qifficult economic times have caused an increase in the foreclosure rate of home mortgages. Statistics from the Penn Bank and Trust Company show their monthly foreclo- sure rate is now 1 loan out of every 136 loans. Last month the bank approved 300 loans. a. How many foreclosures would you expect the bank to have last month? b., What is the probapbility of exactly two foreclosures? c.。 What is the probapbility of at least one foreclosure?

第21題~~

(a) Find the average Speed ov piVen ttme intervals: (1 11.2] (8 1 Gi) [LI (8)踢 (Y)「[1, 1.001 (b) Estimate the speeds 婦 21.。 Pr0jettile_ moti0n labalis thrown into the air With a Speed of 40 多/S, its height in feet f seconds ]ater is given Dy 二07 0 (a) Find the average speed for the time perlod beginnlng When z/ 三 2and lasting (3) 0.5 second (1) 0.1 second 0.05 second (iv) 0.01 second Speed when 7 評 2

答案為 看一場電影 吃六個漢堡 為什麼呢？他並沒有給漢堡的錢呀？

漲,漲價到每場 400 元 (就像「隔凡圈1一 在各種數量下都上判了 20 個效用單位,這 最適選擇 (參見〔衷了2) ) ? 為什麼? 了了 ? 假使電影票價大# -樣),而看 將會如何影響消