2014年度前期日程 数学
[19] PC/Chrome
2014/02/26 13:42
数学解答さらすわ
[1]
(1)-t^2+4at+2
(2)-√2≦t≦1
(3)
最大値
-4√2 (a<-√2/2)
4a^2+2 (-√2/2≦a<1/2)
4a+1 (1/2≦a)
最小値
4a+1 (a<(1-√2)/4)
-4√2a ((1-√2)/4≦a)
2014/02/26 13:42
数学解答さらすわ
[1]
(1)-t^2+4at+2
(2)-√2≦t≦1
(3)
最大値
-4√2 (a<-√2/2)
4a^2+2 (-√2/2≦a<1/2)
4a+1 (1/2≦a)
最小値
4a+1 (a<(1-√2)/4)
-4√2a ((1-√2)/4≦a)
[21] PC/Chrome
2014/02/26 13:47
[3]
(1)a=6,b=0,c=-4
(2)1/12{{3,1},{6,-2}}
(3)1/7{
{6*3^n-(-4)^n, 3^n-(-4)^n},
{6*3^n-6*(-4)^n, 3^n+6*(-4)^n}
}
(4)1/(7*2^n){
{6*10^n+3(-11)^n, 10^n-(-11)^n},
{6*10^n-6*(-11)^n, 10^n+6*(-11)^n}
}
2014/02/26 13:47
[3]
(1)a=6,b=0,c=-4
(2)1/12{{3,1},{6,-2}}
(3)1/7{
{6*3^n-(-4)^n, 3^n-(-4)^n},
{6*3^n-6*(-4)^n, 3^n+6*(-4)^n}
}
(4)1/(7*2^n){
{6*10^n+3(-11)^n, 10^n-(-11)^n},
{6*10^n-6*(-11)^n, 10^n+6*(-11)^n}
}
[22] PC/Chrome
2014/02/26 13:48
[4]
(1)
極大値 2 (x=0)
極小値 -4e^(-3/2) (x=±√6/2)
(2)
-1/2ae^(-a^2)+1/2I(a)
(3)
2√2e^(-1/2)-10e^(-25)
2014/02/26 13:48
[4]
(1)
極大値 2 (x=0)
極小値 -4e^(-3/2) (x=±√6/2)
(2)
-1/2ae^(-a^2)+1/2I(a)
(3)
2√2e^(-1/2)-10e^(-25)
[23] PC/Chrome
2014/02/26 13:54
[5]
(1)
(左辺〕
=|∫-(x^2)^(n+1)/(1+x^2)|dx
≦∫|x^(2n+2)/(1+x^2)| dx
≦∫x^(2n+2)dx
=1/(2n+3) (証明終)
(2)
1-π/4
(3)
anの被積分関数を等比数列の和の公式で分解すると
an
=∫(x^2-x^4+x^6-…+(-1)^(n-1)x^(2n))dx
=1/3-1/5+1/7-…+(-1)^(n-1)/(2n+1) (証明終)
(4)
(1)の不等式でn→∞ではさみうちの原理
lim an=1-π/4
2014/02/26 13:54
[5]
(1)
(左辺〕
=|∫-(x^2)^(n+1)/(1+x^2)|dx
≦∫|x^(2n+2)/(1+x^2)| dx
≦∫x^(2n+2)dx
=1/(2n+3) (証明終)
(2)
1-π/4
(3)
anの被積分関数を等比数列の和の公式で分解すると
an
=∫(x^2-x^4+x^6-…+(-1)^(n-1)x^(2n))dx
=1/3-1/5+1/7-…+(-1)^(n-1)/(2n+1) (証明終)
(4)
(1)の不等式でn→∞ではさみうちの原理
lim an=1-π/4
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