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= (S. 40. WORKING MOTHERS The percentage of mothers who work qutside the home and have children younger than 6 years old is approximated by the function sti deri 10205 hindi P(t) = 33.55(t + 5) 0.205 (0 < t < 32) where t is measured in years, with t = O corresponding to at the beginning of 1980. Compute P"(20), and interpret . 19 Source: U.S. Bureau of Labor Statistics. raph fapp your result

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OUTSOUNDS 39. EFFECT OF DEMAND FOR SMOKE ALARMS ON PRICE The demand function for the Sentinel smoke alarm is given by - 30 p = d(x) = 0.02x2 + 1 Bibs ist bowo 101 zigoloidla where x is the quantity demanded (in units of a thousand) and p is the unit price in dollars. Use differ- entials to estimate the change in the price p when the quantity demanded changes from 5000 to 5500 units per week.

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- MANUFACTURING At a certain factory, Output Q is related to inputs x and y by the equation y Q = 2x2 + 3x?y2 + (1 + y)3 If the current levels of input are x = 30 and y 20, use calculus to estimate the change in input y that should be made to offset a decrease of 0.8 unit in input x so that output will be maintained at its current level. -

請問這題怎麼解，感謝🙏 （（附答案

41. SUPPLY RATE When the price of certain commodity is p dollars per unit, the manufacturer P is willing to supply x hundred units, where 3p2 - x2 = 12 How fast is the supply changing when the price is $4 per unit and is increasing at the rate of 87 cents per month?

89題 謝謝

18 = volume increasing at this is 39. Bone mass In Example 1.1.6 we found an expression for the mass m of a human femur of length L in terms of the outer radius r, the inner radius rin, and their ratio k = lin/r. More generally, if the bone density is p, measured in g/cm°, then bone mass is given by the equation trạL[p - (0 - 1)k?] - - m = It may happen that both p and k change with age, t. P (a) If p changes during aging, find an expression for the rate of change of m with respect to t. (b) If k changes during aging, find an expression for the rate of change of m with respect to t.

61的 a 謝謝

61. Under certain circumstances a rumor spreads according to the equation 1 p(t) = 1 + ae -kt where p(t) is the proportion of the population that has heard the rumor at time t and a and k are positive constants. (a) Find lim,-- p(t). a

第52.自己算了一個跟解答很接近的答案，但還是不知道哪裡不對，求解過程🙏感謝（附解答）

Evaluating a Definite Integral In Exercise KO 47-52, evaluate the definite integral. 63. C! the and tial x(x2 + 1) dx 47. 2x2x3 + 1 dx 48. 1 1 49. 1 • dx 、+ 1 (2x + 1 so. S tant contra dx x(1 + [atta de 51. [ are de 、 。 64.0 es 03/ 52. 1 dx 13 72

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r 50. WATER POLLUTION A circular oil slick spreads in such a way that its radius is increasing at the rate of 20 ft/hr. How fast is the area of the slick changing when the radius is 200 feet? EXERCISE 50

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where ci n n Writing a Limit as a Definite Integral In Exercises 7–10, write the limit as a definite integral on the given interval, is any point in the ith subinterval. 7. lim § (30; + 10) Ax; 3c 8. lim Ë Vc? + 4 Ax; [-1,5] [O, 3] 9. lim Š 10. lim § (2-4 sin c;) Ax; [1, 5] [0, 1] A»0 n n 3 1 + Ax; 141-0 ||A||→0 i=1

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8. (10%) A ladder 13 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 2 fts, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 5 feet from the wall?