2026 Introduction to University Math 03

Transcript

1. pineapple.cc ௕࡚େֶ৘ใσʔλՊֶ෦ େֶ਺ֶೖ໳
    Introduction to University Mathematics
2. pineapple.cc How to take notes w ܗࣜΛܾΊΔ
   w ݟग़͠Λ͚ͭΔ
   w ϖʔδʹςʔϚ
   w Օ৚ॻ͖ʹ͢Δ
   w ༨നΛ࢒͢ ϊʔτͷऔΓํ Life Hacker
3. pineapple.cc ߨٛͷਐΊํʢୈճʙୈճʣ Agenda (Day 2 to Day 8) w େֶ਺ֶ΁ͷೖ໳
   Introduction to University Mathematics ⭐⭐
   w ਺ֶΛ޷͖ʹͳΔ࿩
   Stories about math that makes you fun ⭐
   w ܭࢉػՊֶʢ৘ใՊֶʣ΁ͷڮ౉͠
   A bridge to computer science ⭐⭐⭐
4. pineapple.cc ධՁ Credits w ग़੮
   Attendance
   w ΫΠζͱϛχϨϙʔτ
   Quiz and mini report
   w Ϩϙʔτʢ೚ҙʣ
   Report (optional) w ఺ʢ2ʣ఺ʢ2ʣ
   50 points (Q1) + 50 points (Q2)
5. pineapple.cc ࣭໰
   ʢ೥݄೔ʣ👉-"$4 Question 02 (14th April 2026) 👉LACS w ͳͥະ஌਺ΛYͰදݱ͢Δͷʁ
   Why is ‘x’ unknown?
   w 1⃣ΞϥϏΞޠͷʮະ஌ͷ΋ͷʯͷൃԻʹରԠ͢Δจࣈ͕εϖΠϯޠʹແ͔͔ͬͨ Β
   Because there wasn’t corresponding letter in Spanish.
   w 2⃣จষͰ͋·Γ࢖Θͳ͍จࣈ͔ͩΒ
   Because the letter ‘x’ is less popular than average.
   w 3⃣͔͕ͨͪ❌ͱࣅ͍ͯΔ͔Β
   Because the letter ‘x’ looks like a cross.
   w 4⃣ͦͷଞɾΘ͔Βͳ͍
   Other/Don’t know.
6. pineapple.cc ࣭໰
   ʢ೥݄೔ʣ👉-"$4 Question 02 (14th April 2026) 👉LACS w ͳͥະ஌਺ΛYͰදݱ͢Δͷʁ
   Why is ‘x’ unknown?
   w 1⃣ΞϥϏΞޠͷʮະ஌ͷ΋ͷʯͷൃԻʹରԠ͢Δจࣈ͕εϖΠϯޠʹແ͔͔ͬͨ Β
   Because there wasn’t corresponding letter in Spanish.
   w 2⃣จষͰ͋·Γ࢖Θͳ͍จࣈ͔ͩΒ
   Because the letter ‘x’ is less popular than average.
   w 3⃣͔͕ͨͪ❌ͱࣅ͍ͯΔ͔Β
   Because the letter ‘x’ looks like a cross.
   w 4⃣ͦͷଞɾΘ͔Βͳ͍
   Other/Don’t know.
7. pineapple.cc ؔ਺
   function
14. pineapple.cc ౳߸
    equal sign
16. pineapple.cc a = b a ≜ b a ≡ b
17. pineapple.cc ۃݶ
    limit
18. pineapple.cc θϊϯͷύϥυοΫε ඈΜͰ͍Δ໼͸ࢭ·͍ͬͯΔ
24. pineapple.cc {an } ≜ {a1 , a2 , a3 , …} a ≜ [a1 , a2 , a3 , …]
25. pineapple.cc lim n→∞ an = l
26. pineapple.cc ͨͱ͑͹ʜʜ
27. pineapple.cc {an } ≜ {1, 1 2 , 1 4 , …}
28. pineapple.cc {an } ≜ { 1 2n−1 }
29. pineapple.cc lim n→∞ an = 0
30. pineapple.cc {an } ≜ {1, − 1 3 , 1 5 , − 1 7 , 1 9 , …}
31. pineapple.cc {an } ≜ { (−1)n−1 2(n − 1) + 1}
32. pineapple.cc ࿅श໰୊
33. pineapple.cc 1, 1 2 , 1 3 , …, 1 n , …
34. pineapple.cc lim n→∞ 1 n = 0
35. pineapple.cc 2, 3 2 , 4 3 , …, n + 1 n , …
36. pineapple.cc lim n→∞ n + 1 n = lim n→∞ (1 + 1 n) = 1 + 0 = 1
37. pineapple.cc 1,4,…, n2, …
38. pineapple.cc lim n→∞ n2 = ∞
39. pineapple.cc 2,2,…,3n − n2, …
40. pineapple.cc lim n→∞ (3n − n2) = − ∞
41. pineapple.cc sn ≜ n ∑ k=1 ak , n ∈ {1,2,3,…}
42. pineapple.cc {sn } ≜ {s1 , s2 , s3 , …}
43. pineapple.cc lim n→∞ sn = S
44. pineapple.cc lim n→∞ n ∑ k=1 ak = S
45. pineapple.cc ∞ ∑ k=1 ak = S
46. pineapple.cc ͨͱ͑͹ʜʜ
47. pineapple.cc {an } ≜ {1, 1 2 , 1 4 , …}
48. pineapple.cc {an } ≜ { 1 2n−1 }
49. pineapple.cc ∞ ∑ k=1 ak = 2
50. pineapple.cc {an } ≜ {1, − 1 3 , 1 5 , − 1 7 , 1 9 , …}
51. pineapple.cc {an } ≜ { (−1)n−1 2(n − 1) + 1}
52. pineapple.cc ∞ ∑ k=1 ak = π 4
53. pineapple.cc 1 − 1 3 + 1 5 − 1 7 + 1 9 − … = π 4
54. pineapple.cc lim x→∞ f(x) = l
56. pineapple.cc lim x→a f(x) = l
58. pineapple.cc ͨͱ͑͹ʜʜ
59. pineapple.cc f(x) ≜ sin(x) x
60. pineapple.cc sinc(x) ≜ sin(x) x
61. pineapple.cc lim n→∞ kan = kα lim n→∞ {an ± bn} = α ± β lim n→∞ an bn = αβ lim n→∞ an bn = α β ͨͩ͠β ≠ 0
62. pineapple.cc lim n→∞ kan = kα = k lim n→∞ an f(kx) = kf(x)
63. pineapple.cc lim n→∞ {an ± bn} = α ± β = lim n→∞ an ± lim n→∞ bn f(x ± y) = f(x) ± f(y)
64. pineapple.cc f(kx + ly) = kf(x) + lf(y)
65. pineapple.cc
66. pineapple.cc 1 : 1 1 + 5 2 : 1 2 : 1 1 + 2 : 1 3 + 13 2 : 1 n + n2 + 4 2 : 1
67. pineapple.cc ਺஋ղੳͷੈք
68. pineapple.cc ax2 + bx + c = 0 x = −b ± b2 − 4ac 2a
69. pineapple.cc x2 + 2bx + c = 0 x = − b ± b2 − c
70. pineapple.cc x = − b ± b2 − c b > 0, c > 0, b ≫ c What if…
71. pineapple.cc x = − c b + b2 − c
72. pineapple.cc ࣭໰
    ʢ೥݄೔ʣ Question 03 (21st April 2026) w ϑΟϘφον਺ͷྡ઀߲ͷ঎ͷۃݶ͸ʁ
    What is the limit of consecutive quotations of the Fibonacci sequence?
    w 1⃣ԫۚൺ
    ʜ
    Golden ratio.
    w 2⃣നۜൺ
    ʜ
    Silver ratio.
    w 3⃣੨ಔൺ
    ʜ
    Bronze ratio.
    w 4⃣ͦͷଞɾΘ͔Βͳ͍
    Other/Don’t know.