7. A function is said to be unbounded on the interval (a, b) if (a) Prove that log x is unbounded on (0, 1). (b) Prove that there exists c E R such that x2 - 2x + 1 g(x) = (x - c)2 is unbounded on (1/2, 3/2).5. We say that a function f : R - R is continuous at a E R if limr-a f(x) = f(a). Let x2 sin(2), ifx # 0 f (x) = 0. if x = 0. Is f continuous at r = 0? 6. We say that a sequence (Tn ) is bounded if IM E R s.t. Vn EN, Jan| SM. Prove that if a sequence (@,) converges to 0, then (T, ) is bounded