求3 4 曲線長度

((( 本即肖恩/// = - = = = > 1 13.4.9. 求曲線在指定範圍中的長度 (1) y=xi, x = 0, x = 1 (c0=1 (2) y = x3, x = 0, x=1 (3) y = e", x = 0, x = 1 (4) y = 1, 1 = -1, 1 = 1 y = , x=1 (Hint: (1) (2)互為反函數.) - ( - et te- x 2 1 C 1 9

求6 曲線下面積🙏

IT (2) x = y², x = y + 2 (4) 4x2 + y = 4, x4 + y = 1, y > 0 24 (6) x = tan2 tany, x= - tan² y, -1 <y < , X << - 2 ,

求解

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.

求解 1 2

習題3.3.23.計算題 (1) / VI - 2² de / ( 1 x2 dx ( (2) | - √x2 – 1 dx ( 1 ✓ x² – - dx (6) dx (

請問這題怎麼解，感謝🙏

- 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. -

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17合成函數前面有函數怎麼做？

8:20 ul 4G o moodle.chu.edu.tw 2.4節(p.154):7、31 1-22 Differentiate. 7. y = sec 0 tan 31. (a) Find an equation of the tangent line to the cury y = 2x sin x at the point (11/2, ). (b) Illustrate part (a) by graphing the curve and the line on the same screen. 2.5節(p.162):17、31 7-48 Find the derivative of the function. 17. h(v) = vž1 + y2 31. y = 1 + sinx COS 2.6節(p.170):31 (本題除了算出切線方程式 要用電腦畫出隱函數曲線與切線) 31. x² + y2 = (2x² + 2y? – x)?, (0,5) (cardioid) YA D 2.9節(p.197) :31、35 31-36 Use a linear approximation (or differentials) to est the given number. 31. (1.999) 35. tan 2° +

求解！！！急！！！

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

9）想問中間值那個什麼的是怎麼算？ 網路上的定義搜不到 謝謝

9-12 Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. *10 1/2 9. 8,5°/x3 + 1dx, n=4 , 10. ("* cos*x dx, n= 4 4 12 JO

請問這兩題怎麼解，謝謝🙏

SO SO WON TO In Exercises 37 and 38, use implicit differentiation to dy find the second derivative dr2 37. x2 + 3y2 = 5 38. xy + y2 = 1 1