Mathematics

Problem

Let

h(x)=x\ln x

be defined on the half-open interval

(0,4]

. a. (i) Evaluate

\displaystyle \lim_{x\to 0^{+}} x\ln x

. b. (ii) Find all critical points of

h

(0,4]

. c. (iii) Using the information from parts (i) and (ii), determine the absolute minimum and absolute maximum values of

h

(0,4]

, specifying the points (or limit point) where they occur.