MathDB

For positive real numbers

a,\ b

, two graphs of the function :

x^a

and

\ln bx

have a tangency of point. (1) Let

(s,\ t)

be the tangency of point, express this in terms of

a

, then express

b

as the function of

a

. (2) For

h

with

0 < h < s

, denote the area as

A(h)

of the domain bounded by the line x \equal{} h and two curves y \equal{} x^a,\ y \equal{} \ln bx. Express

\lim_{h\rightarrow 0} A(h)

in terms of

a

Problem Statement