= = = = = = 1, 000, 000, 000, = = 2 2 = = = = a,
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- あいぞう おえづか
- 5 years ago
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1 , 682, 574, 402 = , two to the hundred n n, n 2, n 3,... n
2 = = = = = = 1, 000, 000, 000, = = 2 2 = = = = a, aq, aq 2,... 2, 2 7, 2 7 2, t km 500 = km 2 10 = = , 1000 (M 9.0) (M 7.9) M 8.4
3 1 0.02g) = 2 2 = = 2 3 = = 1, g) 2 20 = 1, 048, kg) 2 30 = 1, 073, 643, t) ,000 t) t % (1.1) 7 = (1.1) 8 = % 114% 12% 14%
4 50%, 1364% 2. n = 1, 2, 3,... 2 n 2 5 = = = = = =? 2 1 =? 2 2 =? 2 3 =?? 2 3 = = = = = = 1 4 = a n a 0 = 1, a n = 1 a n m, n a m a n = a m+n (a m ) n = a mn
5 m n m, n 1µ = 10 3 mm = 10 6 m 0.1 mµ = m = m m g g g g b g b 2 g, b 3 g,..., n b n g
6 b 2 1 1/ /4 = /1000 ( / % 1/2 1/3 1/2 x (1 + x) (1 + x) 2 = 1.1 1/n 1/n x (1 + x) n = 1.1 b n = a b n a a n p 1/n n 1 + p 1 m/n n (1 + p) m 1 1/3 1/ 3 2 m/n 1/ n 2 m n a x 0 x n 0 > a a > 1 x 0 = a x 1 = (n 1)xn 0 + a nx n 1 0 x 2 = (n 1)xn 1 + a nx n 1 1 x 3, x 4, x 5,... n a y = x n
7 (x, x n ) x n = 2, a = 2 x 0 = 2 x 1 = x x 0 = 3 2 = 1.5 x 2 = x x 1 = = x 3 = x x 2 = = x x 2, x 3, x 4 x 5 x 6 y = x n n m π a n n a n 1 = 1 0 < a < b n a < n b n a m = ( n a) m n 1/a = 1/ n a a > 1, m > n m a < n a n m a = mn a n a n = a a 1/n = n a = a 1/n, a m/n = n a m a a q q = m/n) a p a q a pq = a p+q = (a p ) q a
8 q = m/n a q a p a q = a p+q (a p ) q = a pq a 0 = 1, a p = 1/a p a > 1, p > q a p > a q. 4. a > 0 x y = a x a = 2 y = a x a > 1 a = 2 x = 0 y = 1 x y = a x x y = a x x x + h a x+h = a x a h a x a x (a h 1) x h a x a x (x, a x ) (x + h, a x+h ) y a x 0 < a < 1 a x x a x x x + h a x a x a = 1/b b > 1 a x = 1/b x a = 1 a x 10 % 5 % b 1 + b b/2 ( 1 + b ) 2 = 1 + b + b2 2 4 > 1 + b 1/4 b/4 1/n b/n n
9 b x a = 1 + b > 1 a x x x + h h a x (a h 1) h a x ah 1 h h a x h a h 1 h h a h 1 h a = 1 + b > 1, h = 1/n h = 1/n a h 1 a 1 = b n(a 1/n 1) b b a < n(a1/n 1) < b y = a x h = 1/mn 1/mn 1/n 1/n 1/mn n(a 1/n 1)a 1/n n(a 1/n 1) h h (0, 1) (h, a h ) a (0, 1) b a y = a x x = 0 a, h a h 1 h a e
10 n 1/n 1/n a ( ) n n ( e = lim ) n n n ( e = lim ) n n n e e n n! = 1 2 n n 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720, 7! = 5040, 8! = 40320, 9! = , 10! = e e = ! + 1 2! + 1 3! + 1 4! + 1 5! + = n! n ! e ! e e 1 b a = 1 + b = e c c c a log e a 1/n n(a 1/n 1) = n(e c/n 1) = c(n/c)(e c/n 1) h = c/n c eh 1 h
11 h 0 c c = log e (1 + b) H h 2 h/h 2 = e c c = log e 2 2 h/h = e ch/h 1 e ch/h h = e ch/h c H ech/h 1 ch/h ch/h c/h c H = log e 2 H = H g
26 11 20 H20,H25 26 11 20 9 2014in (H24) 9 2014in (H2223,25) 34 (H2223,25) 9 2014in 26 11 20 9 2014in (H2223) (H2223,25) HAPPY 9 2014in (H2225) 5 6 50kg 60kg 17 6 50kg 60kg 71 1 1415 50kg 26 11 20 9 2014in
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春期講座 ~ 極限 1 1, 1 2, 1 3, 1 4,, 1 n, n n {a n } n a n α {a n } α {a n } α lim an = α n a n α α {a n } {a n } {a n } 1. a n = 2 n {a n } 2, 4, 8, 16, 32, n a n {a n } {a n } 2. a n = 10n + 1 {a n } lim an
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2012 IA 8 I 1 10 10 29 1. [0, 1] n x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 2. 1 x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 1 0 f(x)dx 3. < b < c [, c] b [, c] 4. [, b] f(x) 1 f(x) 1 f(x) [, b] 5.
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