全文
[ 東京工業大学 1969 年 ６ ]
0 x y のとき， 2 , 2
y x
x y
x e y e の大小関係を調べよ。
0 x y より 2 0
y
x ex である。
2 2
2 x
x y
y
y x
y x
y e y
x e x e
について考える。
y t
x とおき，
1
2 ( )
t t
t e f t
おくと，
1 1
2
2
´( ) 2 2 1
t t
t t
f t te t e
t
ここで，0 x y より y 1
x である。
よって，①と f(1) 1 であることから t1 において ( ) y 1 f t f
x
したがって
2
2
1
x y y x
y e x e
が成り立つので 2 2
y x
x y
x e y e である。
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