1 1.1 Excel Excel Excel log 1, log 2, log 3,, log 10 e = ln 10 log cm 1mm 1 10 =0.1mm = f(x) f(x) = n
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- しほこ もちやま
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2 . n a n S n a k lim n a n+1 a n < 1. a n n a n a n+1 n1 a n 0 n a n S n a k n N n a n+1 a n < 0 a n > a n+1 n n+1 S a k S n a k S n+1 a k ln1 + x) fx) ln1 + x) f n) x) f n) x) 1) n 1 n 1)!1 + x) n x 0 f n) 0) 1) n 1 n 1)! ln1 + x) n 1) k 1 k 1)! x k + R n+1 x) k! n 1) k 1 x k + R n+1 x) k
3 a n 1)n 1 x n n lim a n+1 1) n n a n lim n 1) n 1 n lim n n n + 1 x x n+1 xn+1 1 < x < 1 n R n+1 x) ln1 + x) 1) k 1 x k k 1) k 1 x k k kn+1 x k k kn+1 1 n + 1 kn+1 x k 1 n + 1 x n+1 1 x x x n
4 4 ln 1 + x 1 x ln 1 + x 1 x ln1 + x) ln1 x) n 1) k 1 x k + R n+1 x) k n 1) k 1 x) k + T n+1 x) k n 1 k xk + T n+1 x) ln 1 + x 1 x ln1 + x) ln1 x) n ) 1) k 1 n x k + R n+1 x) k n 1 k 1 xk 1 + R n+1 x) T n+1 x) n n ln 1 + x n 1 x 1 k 1 xk 1 + U n+1 x) 1 b n n 1 xn 1 lim b n+1 1 b n lim n+1 xn+1 n 1 n 1 xn 1 lim n 1 n n + 1 x n x ) 1 k xk + T n+1 x) 1 < x < 1 4
5 U n+1 x) ln 1 + x n 1 x 1 k 1 xk 1 1 k 1 xk 1 kn+1 n + 1 kn+1 n + 1 x n+1 1 x x k 1 x 5 x x 1 ) ln 1 + x 1 x 1 < x < 1 1 < 1 + x 1 x < log 1, log, log,, log log 1 0 log log log 4 log ) 00 log 00 + log + ln )) ln )) 5
6 log log 1 log 9 1 log 1 1 ) 1 log + log 1 1 )) )) 1 log 4 log log 5 1 log 1 + ln 1 1 ln log 6 log + log log 7 log 7 1 log 49 1 log 1 1 ) 1 log + log 1 1 )) 1 log + log 5 + log 1 1 )) 1 log + ln )) 1 1 ln log 8 log log 9 log log 1 ln ), ln 1 1 ), ln 1 1 ), ln 00 6
7 ln ln ln 1 ln 00 1 ln ) 4 1 ln 4 + ln 00 ) 4 1 ln ln 4 ) 00 1 ln ln )) 00 ln ) ln 00 ln ), ln 1 1 ), ln 1 1 ) ln1 + x) 00 ln ln 1 + x 1 x 6 ln ) ln1 + x) x 4 00 R n+1 x) 1 n + 1 x n+1 1 x 1 n n
8 n R n+1 x) < n ln ) ) n ) n δ 0 δ ln )
9 7 ln 1 1 ) 7.1 ln1 + x) x 1 R n+1 x) 1 n + 1 x n+1 1 x 1 n n n R n+1 x) n ln 1 1 ) 1 1 ) 1 1 )
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11 8. n ln 1 1 ) ) 8. n δ δ ln 1 1 ) ln x 1 x x 1 ln 1 + x 1 x x 1 U n+1 x) n + 1 x n+1 1 x n n+1 )
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13 ln ln ln ln ) 00 [0.6914, ] + [ , 0.07] [ , ] ln [.0546,.05878] [.054,.059] ln 11 log log 1 + ln )) ln 0. + [ [0.07, ] [.054,.059] , [0.097, 0.001] log ] 1 log log ln 1 1 ln )) [ 0.56, 0.5] [.054,.059] [ ] 0.5, [0.477, ] 1
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第18回海岸シンポジウム報告書
2011.6.25 2011.6.26 L1 2011.6.27 L2 2011.7.6 2011.12.7 2011.10-12 2011.9-10 2012.3.9 23 2012.4, 2013.8.30 2012.6.13 2013.9 2011.7-2011.12-2012.4 2011.12.27 2013.9 1m30 1 2 3 4 5 6 m 5.0m 2.0m -5.0m 1.0m
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2010 II / y = e x y = log x = log e x 2. ( e x ) = e x 3. ( ) log x = 1 x 1.2 Warming Up 1 u = log a M a u = M a 0
2010 II 6 10.11.15/ 10.11.11 1 1 5.6 1.1 1. y = e x y = log x = log e x 2. e x ) = e x 3. ) log x = 1 x 1.2 Warming Up 1 u = log a M a u = M a 0 log a 1 a 1 log a a a r+s log a M + log a N 1 0 a 1 a r
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