MATH 321 Midterm: MATH 321 2016 Winter Test 2
Document Summary
Be sure that this examination has 12 pages including this cover. No calculators, notes, or other aids are allowed. Z a (b) equicontinuity (c) convergence in the mean. Answer true (with proof) or false (with speci c counterexample): (a) If f is monotonic on [a, b], then f is riemann integrable on [a, b]. (b) let f be riemann integrable on [0, 1]. Then there is a c [a, b] such that f (c) = r 1. 0 f (t) dt. (c) let f be riemann integrable on [a, b]. Then the function f : [a, b] ir de ned by a f (t) dt is riemann integrable on [a, b]. Let a < c < b and let f : (a, b) ir be continuous on (a, b) and di erentiable on (a, c) and on (c, b). Prove that f is di erentiable at x = c and that f (x) is continuous at x = c.
