想請問2,3(a),4,5(b)的詳解 謝謝🙏

2. (12%) Find ∞ [-1,1] (a) Ui=1 -120 №b) n (1-1) (6) = 1 11. [1]) = [1-1,1] (c) i=1 $(dina (i,∞) i=1

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) =

想問第4題畫線處 分母(tan²x)-1 =(sin²x/cos²x)-1 =(sin²x-cos²x)/cos²x 為什麼把1/cos²x移到分子以後 分母不是sin²x-cos²x ? 感謝！

x² Example 4 Find lim x 0 sec X 1 SOLUTION The evaluation of this limit requires a little imagination. Since both the numerator and denominator tend to zero as x tends to zero, it is not clear what happens to the fraction. However, we can rewrite the fraction in a more amenable form by multiplying both numerator and denominator by sec x + 1. x2 x² sec x 1 lim x-0 secx 1 - = = x2 sec x 1 - x² (secx + 1) sec² x 1 lim (sin x-0 sin x sec x + 1 sec x + 1) - = Since each of these factors has a limit as x tends to 0, the fraction we began with has a limit: = x² (secx + 1) tan² x - 1 x² cos²x(secx + 1) sin² X 2 (*) ² (cos²x)(secx + 1). 2 ·lim cos²x lim (secx + 1) = (1)(1)(2) = 2. x→0 x ●

這個(c)的 inverse reciprocal trigonometric functions 是指什麼？(hahaha)

In a similar manner, one can define the 'arccosine' and 'arctangent' functions by 'restricting the domains'. The following table summarizes the domains and ranges of these inverse functions. Function Domain Range Function f(x) = sin¯¹(x)| (-1,1)|(−½, 3) || f(x) = sec¯¹(x) f(x) = cos ¹(x) [−1,1] f(x) = tan-¹(x) [0, π] Domain Range R (-)|| f(x) = cot-¹(x) x2! [-7,7- XZ1 OY f(x) = csc¯¹(x) 85-1 xs-1 but fuxito Exercise 4. (a) Sketch the graph y = tan-¹(x) (b) From (a), write down lim tan-¹(r) and lim tan-¹(x). x48 8118 (c) Look up the relevant section in the textbook (Stewart), write down the domains and ranges of the 'inverse reciprocal trigonometric functions' on the right hand side of the above table.

求助幫忙 目的是讀入資料，依性別計算身高、體重、年齡的平均，將結果寫入csv 檔案 現在目前我已經把資料成功讀入了，但到計算平均就卡住了 請各位大神幫我看看是那邊出錯了 感謝🙏

} ] v 20 秒 0 秒 from google. colab import drive drive. mount('/content/drive') Mounted at /content/drive [6] import pandas as pd data = pd. read_csv('/dataset_1 (3).csv') print(data) 0 1 2 3 4 539 540 541 542 543 height; "weight"; "age"; "male" 151.765;47.8256065;63;1 139.7;36.4858065:63:0 136.525;31.864838;65;0 156.845;53. 0419145;41;1 145. 415;41. 276872;51;0 145. 415;31. 127751;17;1 162.56;52. 16308;31;1 156. 21;54. 0624965;21;0 71. 12;8. 051258;0;1 158.75;52. 5316235;68;1 [544 rows x 1 columns]

請教這題如何計算

1. 1.1 建立× y的 迴歸方程式 xy 1 25 2 45 3 55 4 65 5 80 9 90 1.2 當x=10 時 推估y值 (class 8)

泰勒多項式

In Exercises 3-4, find the Taylor or Maclaurin polynomial Pn(x) for the function f with the given values of c and n. Then give a bound on the error that is incurred if Pn(x) is used to approximate f(x) on the given interval. 3. f(x) = ²x, c=1, n = 4, [1, 1.1] 4. f(x) = ln(x + 1), n = 3. [2, 4] c = 3,

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七、判断级数(-1)^" 1-1 Inn 的敛散性,如果收敛是条件收敛还是绝对收敛,(8分) = 0 A

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