さくらの個別指導 ( さくら教育研究所 ) a a n n A m n 1 a m a n = a m+n 2 (a m ) n = a mn 3 (ab) n = a n b n a n n = = 3 2, = 3 2+
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1 a a n n A m n a m a n = a m+n (a m ) n = a mn 3 (ab) n = a n b n a n n = 3 +0 = 3, 3 3 = 3 +( ) = = 3 3 =, 3 = 30 3 = 3 0 a 0 a`n a 0 n a 0 = a`n = a n a` = a 83
2 = 0 3 = 0 = = = = =.3 0 ( ) 4 = = (3) () 4 = () ( ) 5 = (3) = (4) = = = 33 = 3 5+( ), = 35 3 = 35 3 = 3 5+ = 3 5 ( ) (3 5 ) = (3 5 ) = 3 5 = 3 (5 ) = 3 5 ( ) (3 5) = (3 5) = 3 5 = 3 5 = 3 5 ( ) a 0 b 0 m n a m a n = a m+n am a n = am`n 3 (a m ) n = a mn 4 (ab) n = a n b n 5. () = 3 () = 0 (3) (3 ) 4 = 3 (4) ( 3 4 ) = 3
3 B n n a a n n = a a n a 3 4 a 5. () 3 = () 3 4 = ( 3) 4 = () ( ) 3 = 8 8 () 4 = ( ) 4 = 6 6 a n y = n ( 0) y y = n ( 0) a n = a a n a a a O n a 5.3 () 3 = = () 3 4 = = 3 a > 0 n a > 0, ( n a) n = a n an = a 5.4 () 3 = () 3 7 = (3) 4 6 =
4 86 5 n a a > 0 b > 0 m n n a n b = n n a a ab n = n b b 3 ( n a) m = n a m 4 m n a = mn a 3 (( n a) m ) n = (( n a) n ) m = a m n a > 0 ( n a) m > 0 ( n a) m = n a m n a m n a m () () = 3 4 = 3 3 = = 3 3 = 3 4 (3) ( 4 5) 3 = = (4) 3 = 3 3 = () () 4 (3) ( 4 5) (4) 4 3
5 C a > 0 a (a ) = a (a ) = a a = a = a a > 0 m n r a n = n a, a m n = ( n a) m = n a m, a`r = a r = = 3 3 = = 5 = 5 = () 4 3 () (3) 5 3 (4) 3 ( ) a > 0 b > 0 r s a r a s = a r+s ar a s = ar`s 3 (a r ) s = a rs 4 (ab) r = a r b r r = 3 s = 3 a 3 a = a 4 6 a 3 6 = 6 a 4 6 a 3 = 6 a 7 = a 7 6 = a 3 + (a 3 ) = 3 a = 6 a = a 6 = a 3
6 () () 3 6 () = = 8 3 = ( 3 ) 3 = 3 3 = = 4 () 3 6 = 3 6 = = = 5.7 () () a > 0 a r r =.44.4,.4,.44,.44, r s n n a n y n = a n a y = n 3 8 = 3 ( ) 3 = 5 = 5 ( ) 5 = n a O n n 0 a n = a a
7 a y = a a A y = a y = y = = 4 = = = = = 3 = =.83 y = O y ( ) y = y y = y y = f() y = f( ) y O y = ( )
8 90 5 y = a a > y y 0 < a < a a O O (0, ) (, a) a > 0 < a < 5.9 ( ) () y = 3 () y = 3 B y = a y = a a > y r < s a r < a s 3 0 < a < y r < s a r > a s a > 0 a r = s a r = a s y y
9 y = y = ( 3 < 0 <.5 ) ( ) 3 > ( ) 0 > ( ) () () ( ) 3 ( 3 3 ) 4 ( 3 ) C 5. ( ) () 4 = 8 () 8 (3) < 3 9 () = 3 4 =( ) = = 3 = 3 () 3 y= 3 ( ) ( ) (3) < 3 3 > y=( 3)
10 ( ) () = 6 () = 6 (3) 3 = 9 (4) 8 = 4 (5) 3 8 (6) ( ) > m km 3.3 0
11 () ( )( ) () ( )( ) 3 () y = () y = + 4 () ( ) = 8 () 7 = 3 (3) ( ) + 3 ( ) 9
12 km 0 3 ( ) () 3 () () () y y 3 O O 4 () = 3 () = (3)
13 y = y A y y = y = q q = q log q 5.7 () 8 = 3 log 8 = 3 () = log = O log q 5. () log 6 = () log 4 = (3) log = 0 y = a y = a M M = a p p p log a M a M log a M M y M 0 < a < log logarithm log a M O a > 0 a M > 0 M = a p log a M = p log a M a > 0 a M > 0
14 () 8 = 3 4 log 3 8 = 4 () log 4 6 = 6 = 4 6=4 4 = 4 = log 4 6 = 5.3 () 9 = 3 log 3 9 = () 5 = 5 log 5 5 = (3) 3 = 4 = log 3 (4) log 4 64 = = log a M = p M = a p log a a p = p 5.9 () log 5 5 = log = 3 log a M M a p () log 3 3 = log3 3 = 5.4 () log 5 () log 5 5 (3) log 3 7 (4) log 6 (5) log 0 0. (6) log 5 5 (7) log 3 (8) log 3 3
15 B a = a 0 a = a log a = 0 log a a = M > 0 N > 0 k log a MN = log a M + log a N log a M N = log a M log a N 3 log a M k = k log a M log a M = p log a N = q log a N = log a N M = a p, N = a q MN = a p a q = a p+q log a MN = p + q = log a M + log a N log a M = p log a N = q M = a p, N = a q M N = ap a q = ap q M log a N = p q = log a M log a N 3 log a M = p M = a p M k = (a p ) k = a kp log a M k = kp = k log a M
16 () log 0 + log 0 5 = log 0 ( 5) = log 0 0 = 4 () log 4 log 3 = log 3 3 = log 8 = log 3 = 3 (3) log log 3 5 log 3 8 = log log 3 5 log = log 3 = log () log 4 + log 4 8 () log 3 log 3 8 (3) log log log 3 (4) log 0 5 log log 0 9 C a log a b c log a b = p b = a p log c b = log c a p log c b = p log c a a log c a 0 p = log c b log c a a b c a c log a b = log c b log c a
17 () log = 3 6 = 4 log 8 6 = log 6 log 8 = log 4 log 3 = 4 3 () log 3 log 3 8 log a log b log 3 log 3 8 = log 3 log 8 log 3 = log 8 = log 3 = () log 4 8 () log 9 3 (3) log 3 log a y = log a a A y = log y = log = y 89 y = y y y y (, y) 3 O y = log 3
18 00 5 y y = Q(t, s) y =. t = log s s = t P(s, t) O Q(t, s) y = P(s, t). P(s, t) Q(t, s) y = y = log a y = a y = y a > y 0 < a < y = a O a y = a O a y = y = log a y = y = log a y (, 0) (a, ) a > 0 < a < 5.8 () y = log 3 () y = log
19 5.. 0 B y = log a y = log a a > 0 < p < q log a p < log a q 3 0 < a < 0 < p < q log a p > log a q p > 0 q > 0 p = q log a p = log a q 5. y = log y 3 log 3 y log log 3 = log 8 3 y = log > 0 O 0 < 8 y = log y = y = log y 4 y = log y
20 0 5 C 5. () log + log ( ) = 3 () log ( ) > () M > 0 N > 0 log a M + log a N = log a MN () > 0 > 0 > log ( ) = 3 ( ) = 3 ( + )( 4) = 0 + > 0 = 4 () log ( ) > log ( ) 4=0 > 0 < 4 < < 5 4 y=log ( ) 5.0 () log ( + 5) + log ( ) = 3 () log ( + ) 3 3
21 =.6 0 6, = n 0 A 0 M M = a 0 n n a < 0 log 0 M n log 0 a log 0 M = log 0 a + log 0 0 n = log 0 a + n a log 0 a log 0.6 = log = log 0 ( ) = log log = = log = log 0 ( ) = log log = = () log () log (3) log a < 0 log 0 a 0 log 0 a <
22 04 5 B N log 0 N N 3 N 00 N < N < 0 3 log 0 0 log 0 N < log log 0 N < 3 n 0 n 5N<0 n n 5log 0 N<n log 0 N < 3 N 3 5. N log 0 N () () 5 (3) log 0 3 = log = 0 log 0 3 = = < log < 0 log < log < log < 3 0 < log 0 = () 0 () 30
23 log 0 = n 0 n n n < 0 0 n n n < n log 0 < 0 9 log 0 n < 0 log 0 log 0 = log 0 = = log 0 = = 33. n n = 30, 3, 3, log 0 3 = n 8 n
24 < M < M log 0 M M 3 0 M 0.00 M < M < 0 3 log 0 M < 3 log 0 M < M < M < M 5 0 log 0 M () log log 4 () log 3 3 log 3
25 6 y = log ( ) () log 3 ( + ) = () log ( ) log 8 log 0 = () log 0 5 ()
26 () () 3 6 y O 3 7 () =, 4 () 0 < 8 () () A () () () 8 () 0.5 4
27 () 3 + = 3 ( ) 9 () (3) ( ) 4 () log log 5 log5 4 () (log 3 + log 4 9)(log log 9 ) 5 log 0 = a log 0 3 = b a b 3 () log 0 () log (3) log 3 (4) log 0 5
28 0 5 6 a b c log a b log b c log c a = 7 () log 0.5 ( + )( + ) = () log 3 ( ) + log 3 ( 7) = 8 log 0 =
29 B 9 () y = + ( 3 3) () y = log ( + ) (0 ) = 0 () = t t () () y = 4 () y = (log 3 ) log 3
30 5 () log 0.5 (3 ) log 0.5 () log ( + ) + log ( ) < 3 M = 3 5 () log 0 M () M
31 ( ) n 4 log 0 = < 0 n 4 5 log 0 = log 0 3 = n < 3 0 < n+ n 0 () > 0 t > 0 () log 3 = t 3 () log 0 M 4 log 0 = log =
32 4 5 () 08 () 3 () 3 () 0 3 () = 3 () (3) 3 4 () 0 () 5 5 () b 3a () 3 (a + b) (3) b a [ 6 = log b log a c b log ] a a a log a log a c (4) a + b 7 () = 0, 3 () = n 00 n > () 4 y 6 () 3 y 0 () t 3t 4 = 0 () = () = () = 3 4 () < 3 () < < 3 3 () ().7 [ ] 4 n = 4 n log 0 < 4 5 n = 3
33 5.4 ()
34 5.5 ()
a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552
3 3.0 a n a n ( ) () a m a n = a m+n () (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 55 3. (n ) a n n a n a n 3 4 = 8 8 3 ( 3) 4 = 8 3 8 ( ) ( ) 3 = 8 8 ( ) 3 n n 4 n n
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2 log 3 9 log 0 0 a log 9 3 2 log 3 9 y 3 y = 9 3 2 = 9 y = 2 0 y = 0 a log 0 0 a = a 9 2 = 3 log 9 3 = 2 a 0 = a = a log a a = log a = 0 log a a =. l
202 7 8 logarithm a y = y a y log a a log a y = log a = ep a y a > 0, a > 0 log 5 25 log 5 25 y y = log 5 25 25 = 5 y 25 25 = 5 3 y = 3 log 5 25 = 3 2 log 3 9 log 0 0 a log 9 3 2 log 3 9 y 3 y = 9 3 2
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2 (1) a = ( 2, 2), b = (1, 2), c = (4, 4) c = l a + k b l, k (2) a = (3, 5) (1) (4, 4) = l( 2, 2) + k(1, 2), (4, 4) = ( 2l + k, 2l 2k) 2l + k = 4, 2l
ABCDEF a = AB, b = a b (1) AC (3) CD (2) AD (4) CE AF B C a A D b F E (1) AC = AB + BC = AB + AO = AB + ( AB + AF) = a + ( a + b) = 2 a + b (2) AD = 2 AO = 2( AB + AF) = 2( a + b) (3) CD = AF = b (4) CE
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卓球の試合への興味度に関する確率論的分析
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福岡大学人文論叢47-3
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加速度センサを用いた図形入力
( ) 2/Sep 09 1 2 1. : ( ) 2. : 2 1. 2. 2 t a 0, a 1,..., a ( ) v 0 t v 0, v 1,..., v n ( ) p 0 t p 0, p 1,..., p n+1 3 Kentaro Yamaguchi@bandainamcogames.co.jp 1 ( ) a i g a i g v 1,..., v n v 0 v i+1
km2であり 土地利用の状況 % % 2 % % % % % % % % % % m m m m km2であり たたら製鉄についてのまとめ
65 1229 1570 5 3 5 2769 1876 1889 9 1892 1927-73 - - 1619 131 2 5500 43 194 1889 1955-1617 3 2 3 1186 2 9 15 1165-74 - 596 300 200 4 888 4 888 11 3 8892 10 2 969 708781782888 729 749 859 877 3 947 3 1523
% 4.4% % 5.0% % 4.5% % 2.7% % 2.0% % 3.6% 5.1% 4.5% 2.6% 3.6%
11 10 12 8.9% 4.4% 2005 9.2% 5.0% 2006 6.5% 4.5% 2007 1.0% 2.7% 2008 1.9% 2.0% 2009 7.3% 3.6% 5.1% 4.5% 2.6% 3.6% 2012 2011 2010 2004 H22.3.27 2011 3 10 2010 9 10 2 128 60 191041 100 100 2011 JR km 89