IUM-02 Limit - Speaker Deck

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pineapple.cc ௕࡚େֶ৘ใσʔλՊֶ෦ େֶ਺ֶೖ໳ Introduction to University Mathematics

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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 ⭐⭐⭐

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pineapple.cc ධՁ Credits w ग़੮Attendance w ΫΠζͱϛχϨϙʔτQuiz and mini report w Ϩϙʔτʢ೚ҙʣReport (optional)

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pineapple.cc ؔ਺function

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pineapple.cc ౳߸equal sign

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pineapple.cc a = b a ≡ b a ≜ b

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pineapple.cc ۃݶlimit

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pineapple.cc θϊϯͷύϥυοΫε ඈΜͰ͍Δ໼͸ࢭ·͍ͬͯΔ

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pineapple.cc {an } ≜ {a1 , a2 , a3 , …}

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pineapple.cc lim n→∞ an = l

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pineapple.cc ͨͱ͑͹ʜʜ

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pineapple.cc {an } ≜ {1, 1 2 , 1 4 , …}

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pineapple.cc {an } ≜ { 1 2n−1 }

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pineapple.cc lim n→∞ an = 0

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pineapple.cc {an } ≜ {1, − 1 3 , 1 5 , − 1 7 , 1 9 , …}

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pineapple.cc {an } ≜ { (−1)n−1 2(n − 1) + 1}

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pineapple.cc lim n→∞ an = 0

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pineapple.cc sn ≜ n ∑ k=1 ak , n ∈ {1,2,3,…}

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pineapple.cc {sn } ≜ {s1 , s2 , s3 , …}

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pineapple.cc lim n→∞ sn = S

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pineapple.cc lim n→∞ n ∑ k=1 ak = S

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pineapple.cc ∞ ∑ k=1 ak = S

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pineapple.cc ͨͱ͑͹ʜʜ

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pineapple.cc {an } ≜ {1, 1 2 , 1 4 , …}

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pineapple.cc {an } ≜ { 1 2n−1 }

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pineapple.cc ∞ ∑ k=1 ak = 2

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pineapple.cc {an } ≜ {1, − 1 3 , 1 5 , − 1 7 , 1 9 , …}

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pineapple.cc {an } ≜ { (−1)n−1 2(n − 1) + 1}

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pineapple.cc ∞ ∑ k=1 ak = π 4

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pineapple.cc 1 − 1 3 + 1 5 − 1 7 + 1 9 − … = π 4

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pineapple.cc lim x→∞ f(x) = l

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pineapple.cc lim x→a f(x) = l

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pineapple.cc ͨͱ͑͹ʜʜ

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pineapple.cc f(x) ≜ sin(x) x

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pineapple.cc sinc(x) ≜ sin(x) x

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pineapple.cc

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pineapple.cc ਺஋ղੳͷੈք

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pineapple.cc x2 + 2bx + c = 0

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pineapple.cc x = − b ± b2 − c b > 0, c > 0, b ≫ c What if…

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pineapple.cc x = − c b + b2 − c

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pineapple.cc @kanaya