求過程 算到最後卡住了

To 1-3 -1 301 | R₂ + ZR₁ Brok: 02 6 1-5 0 - R3-R1 03-924 |-|| R4 +R₁ N 2₁ R₁ - R₂ R3+5R₂ T 0-1 3 1 3 2 01-302 ött 00 32 | 1 。 O 0622 -R2- 0 CONCE 1-3 -1 30 17 000 5-51-4 0000622 200 1-10-1 22 11

求解！謝謝！

Q 0-3. 若函數f(x) = x,則f'(x) 的定義域為 (1).(-1, ∞) (2).[-1,∞) (3)(0,0] (4).以上皆非

求這題～ 答案為為 a .31cm b.866J c.1.15J

ping. What was the initial speed of the bullet? 8.43 A Ballistic Pendulum. A 12.0 g rifle bullet is fired with a speed of 380 m/s into a ballistic pendulum with mass 9.00 kg, suspended from a cord 70.0 cm long (see Example 8.8 in Section 8.3). Compute (a) the vertical height through which the pendulum rises, (b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the wood. 150 kg block is attached A

求這三題（不是很確定答案）

10. Evaluate the following limit: -1 (a) lim lim (1+¹) (c) lim (6--/-) x x→0+ x3 (b) lim x+1-(x - 1)² 9. x1-41-31-21|-||0|||2|3|4

如何從上面的式子推導出an跟an+1的關係式？

By Eq: = (1+1) 9₁+1+" = 9.8-551/1 anti t^ n=0 I auth "} a₁ = 98 (n=0) { | (n+1) Gn+1 = ~= A₂ (4²1) An

請問紅色圈起來的地方是為什麼？ 謝謝🙏

7−(−2+h)— √7−(−2) h −1 −1 √9-h+3 V9+3 My Ax As h→0. = 9-h-3 h 6 = 9-h-3√9-h+3 (9-h)-9 -1 = √9+h+3h(√√9+h+3)¯¯ √√9+h+3² Th ⇒ at P(-2,3) the slope is =

想問第42題

25. lim 8118 27. lim X18 A 29. lim 31. lim 33. lim √x - √√x x→→∞ √√√x + √√x 35. lim 2x²/3 - x1/3 + 7 xxx x8/5 + 3x + √x 37. lim x→∞ x + 1 39. lim x - 3 x→∞ √4x² + 25 1 x→0+ 3x 1-x² 2√x + x¹ 3x - 7 41. lim 1. 2 X-2 X- 43. lim √x² + 1 45. a. lim 3 2x x-8+ x + 8 + 7x 4 x→7 (x-7)² 2 2 46. a. lim x-0+ x1/5 4 2 x-0+ 3x¹/3 B Infinite Limits Find the limits in Exercises 37-48. Write ∞ or -∞ where appropriate. 5 x →0-2x x - 3x 26. lim√√³+x-2 b. lim 2 + √x x→∞ 2 - √x 28. lim 30. lim x¹ + x4 x-xxx-²-x-3 32. lim Vì - 5x + 3 x-∞ 2x + x2/3 - 4 34. lim 36. lim 2 x→0 3x¹/3 xxx +1 2 b. lim x→0 x1/5 4 - 3x3 x-∞ √6 +9 38. lim 40. lim √x² + 1 42. lim x-3x - 3 3x x-5-2x + 10 44. lim -1 x→0 x²(x + 1) 19 lime 1

求解第二題！ （因為圖片要兩題一起看所以順便拍進來了）

§ 1.1 An Intuitive Introduction to Limits For Exercises 1 and 2, use the graph of the function f to determine whether each statement is true or false. Explain.(從圖形決定極限) 1. O lim f(x)=XX/ x→-3+ lim f(x) = 1. x→2 2. a) lim f(x)=1. x-→-3+ e) lim f(x) does not exist. x →4+ c) lim f(x) = 2. x->2 b) lim x->0 flim f(x) = 3. x-5 d) lim f(x) = 3. x-4 f(x) = 2. Xe) lim f(x) does not exist. x →3 lim f(x) = 2. X→4 S b) lim f(x) = f(0). x->>0 d) lim f(x)=3. x->2* y 4 3 234 y = f(x)

求解釋這一題 看不太懂😭

例題:【反函數】 若f(x) = x²,f:[0,3]→[09],求 f(x)的反函數。 2: To9]→{0.3] 解: f(x) = x 在 [0,3]上為1-1 函數,取f'(x) = x,則有 f(f'(x)) = (√x)} = =x, ∀x∈[0,1] 345 S' (f(x))=√x² = =x,∀x∈[0,0],故f(x) 的反函數為」。 f(x)=xx 2:57/9:52 y X

想問上面那題，為什麼區間是0、10？ 從哪裡得出來的

1-6-8 中間值及勘根定理 片 1 例題:【中間值定理】 給函數f(x) = x+x+1,證明必定存在一實數c,使得f(c)=100。 解: 因 f(x) = x+x+1為一個多項式,所以在[0,10]區間上連續 因為f(x) = x* + x+1在閉區間[0,10]上連續, 又(0)=1<100<1001 = f(10) 所以由中間值定理,必定存在一實數c,使得f (c)=100。 ↳s 例題:【勘根定理】 證明方程式x-2x²+x+1=0,在(-1,1)區間內至少有一個實根。 證: