求解微分，後面括弧是答案

(l) 2 2 4 y = x² cos²x X 2 ( = x² = 2x cos²x² - 4x² sin²³x) y = (x+cosX) (1-sinX) (+7= -XX)

請問這題要怎麼算～

1 89. Let f be a function such that f'(x): If 1 + x² 0₁5 2 LIFE AND Qurbliet 1 + x² dig(x) = f(2x + 1), what is g'(x)?sup inslissxs) =

請問這該如何寫，謝謝🙏

din df 70. a. Show that dg d filtzh) = f8 - + the + gh- dx dx dx [Hint : Apply the product rule twice.

請問35、36怎麼解，希望有算式✍🏻，感謝！

b. What is the rate of change of the total cost when the level of production is ten surfboards a day? 35. EFFECT OF ADVERTISING ON PROFIT The quarterly profit (in thousands of dollars) of Cunningham Realty is given by x in = 3.5, 3. alt of P(x) = -*** + 7x + 30 = -ered en by time = - vhen 1 P( -x2 + (0 < x < 50) 3 bos where x (in thousands of dollars) is the amount of money Cunningham spends on advertising per quarter. a. Find P'(x). b. What is the rate of change of Cunningham's quarterly profit if the amount it spends on advertising is $10,000/quarter (x = 10) and $30,000/quarter (x = 30)? 36. DEMAND FOR TENTS The demand function for Sportsman 5 X 7 tents is given by p = f(x) = -0.1x2 – x + 40 where p is measured in dollars and x is measured in units of a thousand. a. Find the average rate of change in the unit price of a tent if the quantity demanded is between 5000 and 5050 tents; between 5000 and 5010 tents. b. What is the rate of change of the unit price if the quan- tity demanded is 5000? t (b). = own at its 2. time s the

可以幫忙看答案是否有誤嗎？謝謝

u. WUP 3. Tablet PCs: Cost, CPU, and Operating System. Refer to Table 1.6. ratio a. What is the average cost for the tablets? 587.9 b. Compare the average cost of tablets with a Windows operating system to the (負銀系) average cost of tablets with an Android operating system. Windows : 133.2, Android: 438.5 c. What percentage of tablets use a CPU manufactured by TI OMAP? 70% d. What percentage of tablets use an Android operating system? 40%

想請問26題如何做，謝謝

- Ym)-1 YmYm-1...7271. = -1 = 20. Show that (1 2) is not a produ 21. (a) If 7. 12....m are transpositions, show that ( (b) Show that o and 0-1 have the same parity for all o in Sn. (c) Show that o and Tot-1 have the same parity for all o and T in Sn: 33. Show that Antun Sn = A, for all n 2 3 (regard Sm C Sn+1 in the usual way). 23. Leto € Sm, o te. If n 23, show that y € Sn exists such that or + yo. (Hint: If ok=1 with k #1, choose m€ {k,1; and take y = (k m).] 24. If o E Sn, show that o2 = e if and only if o is a product of disjoint transpositions. 25. If n23, show that every even permutation in Sn is a product of 3-cycles. 26. Let y be any cycle of length r. If o e Sn, show that oyo-1 is also a cycle of length r. More precisely, if y = (kı k2 okr). kr) show that oyo-1 = (oki ok2 27. (a) Show that (kı kz ... kr) = (ki kr) (kı kr-1)... (kı k2). k2 = (- (b) Show that each o ESn is a product of the transpositions (1 2), (1 3),...,(1 n). (Hint: Each transposition is such a product by (a) and Exercise 26.] (c) Repeat (b) for the transpositions (1 2), (2 3),..., (n-1 n). (Hint: Use (a) and Exercise 26.) (d) If o= (1 2 3 n), show that each element of Sn is a product of the permutations (1 2), o, and 0-1. (Hint: Use (b) and Exercise 26.] 28. Let o = (1 2 3 ... n) be a cycle of length n > 2. (a) If n = 2k, find the factorization of o2 into disjoint cycles. 9 =

第二題的d的積分範圍要怎麼設

6 Kx, lo, 14) 1. (10 points) How many even numbers can be formed from the digits 9, 1,4,5,6, and 9 if each digit can be used only once? 2. (50 points) Let X and Y denote the lengths of life, in years, of two components A and B, respectively, ş! x2 in an electronic system. If the joint density function of these variables is 64 0<x<1-ycl EX,Y) Rx hy 0 < x <1.0<x<1-x: f(x, y) = elsewe jey.301-4)*84f CX74 3 Rxdy * 了 1' Jay You Determine the value k; FED ECX) = 86 x 6xci->)dy cy) 3(1-2) ² (b) Find the marginal distributions, expected values, variances, and covariance of X and Y; dy= 1 (C) Determine whether X and Y are dependent or independent; X(d) Find the probability that the length of life of component A is less than that of component B; X(e) Find the probability that the length of life of component A is greater than one year, given the ar length of life of component B is equal to two year. xcy 1313. (10 points) The probability that a flight departs on time is 0.3; the probability that it arrives on time is 0.3; and the probability that it departs and arrives on time is 0.1. Find the probability that it arrives on time, given that it did not depart on time. ex oin 4. (20 points) The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution -8x76 / le = 1- e 11-e dx x ZO; dv=e 0, f(x) = f'(X) = x < 0. 8 e V= 1 84 (a) Find the probability of waiting less than 10 minutes between successive speeders; hind the wyerane waiting time between successiye speeders spotted by a radar unit. 013-0il u=X -8X -81 -8% ge

經濟問題求解

cc. marginal cost exceeds average revenue. d. price equals marginal revenuee 4和 Amonopolistically competitive firm faces the following demand schedule for its product:川紀 2 明" 應 (怒 且人 外 6 2 線 7 [price 國加世光了光上防到還說9信2] 全生國加還3 9 nti 還 6 | 只 : 上3吧 18人|避24[S242a|8829 30 Thefirm has total fixed costs of $9 and aconstant marginal cost of $3 per unit. The 避 / 2 0 7 firm will maximize profit with 出 歡OOIUNZd 2 1 滲 1人歡到 | 說說只 a. 9 units of output- 以 - : b. 15 units of output- 和 Cc. 21 units of output. 人 d. 30 units of output. 2 員

微積分 這題怎麼解 他是問啥

47 Averoge cosf、 Fora company that manufactures tennis Tackets, the average cost per racket Cis 1 表 語 Where is the number ofrackets produced per hour' What Will the approximate change jn average cost per Tracket be 痊production is increased from 20 per hour to 25 per hour? From 40 per hour to 45 per hour?

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