Napier's Inequality (I)
Napier's Inequality (I)
Napier's inequality: If , then <<.
0<a<b
1
b
lnb-lna
b-a
1
a
Observe that in the graphic, , the slope of the secant line passing through and , is between the slopes of the tangent lines at and .
lnb-lna
b-a
(a,lna)
(b,lnb)
x=b
x=a