(i)     Suppose that f(0)=0 and that, for x ¹ 0,

0 £ f(x) x £ 1

. Show that

- 1 2 £ ó õ 1 -1  f(x) dx £ 1 2 .

(ii)     Suppose that f(0)=0 and that, for x ¹ 0,

0 £ f(x) x2 £ 1

. Show that

0 £ ó õ 1 -1  f(x) dx £ 2 3 .

(iii)     Generalize (i) and (ii) to the case where f(0)=0 and, for x ¹ 0,

0 £ f(x) xn £ 1

where n is a positive integer.