請問24題的解題思路是什麼？看了很久還是不知道從哪裡開始🤔

Finding an Indefinite Integral in Exercises 17–26, find the indefinite integral. 4x² dx 18. dx W] 116 M 19. √1- x² •dx x4 S Juta 20. Invatta Jose 22. Jest - er de dx (4x² + 9 21. -3 (x² + 3) 3/2 dx e2x dx 23. 1 4 + 4x² + x4 dx 2 x² + x + 1 dx xt + 2x² + 1 1 ***

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

請問第16題怎麼寫，感恩🙏

8. M () 12 -31 1 1 In Exercises 9 through 16, find all vertical and horizontal asymptotes of the graph of the given function 3x – 1 X = 10. f(x) 9. f(x) = - x + 2 2 - x 2. 12. f(t) = = t + 2 12 x² + 2 11. f(x) x² + 1 2 + 3t - 5 13. f(t) = 2 - 5t+ 6 5x2 = 14. g(x) = = - x² – 3x - 4 1 1 t 15. h(x) h(x 16. g(t) = = X X 1 V? - 4 In Exercises 17 through 32, sketch the graph of the given function. 17. f(x) = x3 + 3x² – 2 18. f(x) = x - 5.x+ + 9 19. f(x) = x4 + 4x + 4x2 20 - = = flr

31&35都是不存在 不存在要如何判斷

adrant adrant Evaluate the following improper integrals: x dx 28. dx 广 1 29. = -2 (x² – 4) 3x vertical 2 X 30. dx 31. 1.0 • dx (9 - x2) ? x - 1 x² dx 32. si 33. (x – 8) 3 dx (x - 3)2/5 - | r 5 X 1 34. dx 35. dx (x² – 4)² -3 (x + 2)4

請問這個面積要怎麼積啊 答案是8

Y = 24 4x2 + 4 ly=x2 = 解 Y, X X = - X = 2,9 - ::-2, y = 4 , Y 2, y = 4 -1, y = 1 x = 1, y = 1 1 X = = = : = 圖表 3938 25 20 15 10 5

詢問此題微分🙏

2 1-(1+t)? - (+ 12 40. lim - t(1 + t)? 101 t0

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.

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

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° +

第6題求解，謝謝

6. (12%) (a) Find the equation of the line which is parallel to the tangent line to the graph of 2 x y ==+ at the point (2,2) and passes through the point (1,-1). 2 (b) Find the equation of the line which is perpendicular to the line obtained from part (a) and passes through the point (-2,1). y+1=0(2