MATH 410 Final: MATH410_BOYLE-M_FALL1993_0101_FINAL_EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 410
• Professor: All

Document Summary

There are 200 points possible on the nal. 45 of these points were on the take- home part: (20 points) suppose f : [a, b] [a, b] and f is continuous. Prove that lim x 0 f (x) g(x) xnp|x| = 0: (20 ponts) suppose f and g are functions from r to r such that f (x) = g (x) for all x, and f (0) = g(0). Prove that f (x) = g(x) for all x: (20 points) suppose kn is a sequence of nonempty compact sets in r such that for all n, kn contains kn+1. Prove that there is a point which is contained in all of these sets: (25 points) suppose f : [a, b] r is bounded and is continuous at all but nitely many points in [a, b]. Prove that f is integrable: (25 points) suppose ak is a sequence of real numbers such that.