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(a) Show that the function f(x)=x^x is increasing on (e^(-1), infinity) (b) Let f(x) be as...

(a) Show that the function f(x)=x^x is increasing on (e^(-1), infinity)

(b) Let f(x) be as in part (a). If g is the inverse function to f, i.e. f and g satisfy the relation x=g(y) if y=f(x). Find the limit lim(y-->infinity) {g(y)ln(ln(y))} / ln(y). (Hint : L'Hopital's rule)

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