试比较:e的0.5次方和-0.5次方及0.5的e次方和-e次方的大小(无理数e=2.718.)4个要一起比的............................................................................................................................................

Question

试比较:e的0.5次方和-0.5次方及0.5的e次方和-e次方的大小(无理数e=2.718.)
4个要一起比的.........................................................................................................................................................................

Answer 1

e^0.5>1
e^-0.5=1/e^0.5
e^0.5>e^-0.5
0.5^e<1
0.5^-e=1/0.5^e
0.5^e<0.5^-e
0.5^e<0.5^2=0.25
e^-0.5=1/e^0.5
e^0.5<4
1/e^0.5>0.25
0.5^e0.5^-e>e^0.5
得出
0.5^-e>e^0.5>e^-0.5>0.5^e