令f(x) = (lnx)/x,x>1.f(x)‘ =[ (1/x) * x - 1*lnx]/x^2 = (1-lnx)/x^2,
所以f(x)在(1,e)上递增,在[e,正无穷)上递减.
(1)当e>b>a>1时,f(b)>f(a),得到b^a>a^b.
(2)当b>a>e时,f(b) 123 = 120^1.1.
所以说是不确定的.
令f(x) = (lnx)/x,x>1.f(x)‘ =[ (1/x) * x - 1*lnx]/x^2 = (1-lnx)/x^2,
所以f(x)在(1,e)上递增,在[e,正无穷)上递减.
(1)当e>b>a>1时,f(b)>f(a),得到b^a>a^b.
(2)当b>a>e时,f(b) 123 = 120^1.1.
所以说是不确定的.