11/09/30 19:24:21.62
微分法の別の表現
2011年9月30日
以下の式を求めます．
x_{2}-x_{1}/t_{2}-t_{1}=x_{1}/t_{1}
x_{2}, t_{2}に1を代入します．
そして，x_{1},_{1}に1/2を代入します．
{1-(1/2)}/{1-(1/2)}=(1/2)/(1/2)=1
この分母と分子を分母で割ります．
{(1/2)/(1/2)}/{(1/2)/(1/2)}={(1/2)*(2/1)}/{(1/2)*(2/1)}=1/1
この分母と分子を2で割り続けます．
0.5/0.5, 0.25/0.25, ...
855:１３２人目の素数さん
11/09/30 19:24:36.93
計算機で割り続けます．
計算機で割り切れなくなった値をεとします．
0.5/0.5,...,ε/ε
実際の計算では，割り切れなくなった値の一つ前の値を用います．
これにより，分母の下で分子の変化が分かります．
そのため，分母と分子は残して置きましょう．
極限操作したε/εが得られました．
また，前に求めた値x_{1}/t_{1}=(1/2)/(1/2)が得られています．
これらは，1で等しくなります．
x_{1}/t_{1}=(1/2)/(1/2)=ε/ε=1
これは微分法の別の表現に使えそうです．
856:１３２人目の素数さん
11/09/30 19:24:59.88
The different expression of the differentiation
September 30, 2011
I demand the following an expression.
x_{2}-x_{1}/t_{2}-t_{1}=x_{1}/t_{1}
I substitute 1 for x_{2}, t_{2}.
And I substitute 1/2 for x_{1},_{1}.
{1-(1/2)}/{1-(1/2)}=(1/2)/(1/2)=1
I divide this denominator and numerator by a denominator.
{(1/2)/(1/2)}/{(1/2)/(1/2)}={(1/2)*(2/1)}/{(1/2)*(2/1)}=1/1
I continue dividing this denominator and numerator by 2.
0.5/0.5, 0.25/0.25, ...
857:１３２人目の素数さん
11/09/30 19:25:22.17
I continue dividing it with a computer.
I assume the value that was not divisible with a computer ε.
0.5/0.5,...,ε/ε
By the real calculation, I use a value before one of the values that were not divisible.
I in this way understand the change of molecules under the denominator.
Therefore a denominator and the molecules do not finish, and let's put it.
ε/ε which operated a limit was provided.
Moreover, value x_{1}/t_{1}=(1/2)/(1/2) which I found before is provided.
These equal with 1.
x_{1}/t_{1}=(1/2)/(1/2)=ε/ε=1
This seems to be usable in the different expression of the differentiation.
858:１３２人目の素数さん
11/09/30 21:46:28.26
>>857
Mistake
morecules
It is correct．
numerator