94.8

(See attached file for full problem description with equations) --- 94.8 Let be a sequence of functions on E such that where . Let be a nonincreasing sequence of nonnegative numbers that converges to 0. Prove that converges uniformly on E (Hint: See 3.8C) Theorem 3,8C Let be a sequence of real numbers whose partial sums form a bounded sequence, and let be a nonincreasing sequence of nonnegative numbers which converges to 0. Then converges. --- We are using the book of Methods of Real Analysis by Richard Goldberg

95.1

(See attached file for full problem description) We use the book Methods of Real Analysis by Richard Goldberg

95.3

(See attached file for full problem description with equations) --- 9.5-3 Without finding the sum of the series Show that --- We use the book Methods of Real Analysis by Richard Goldberg

93.5

(See attached file for full problem description with equations) --- 9.3-5 Let be a sequence of functions on [a,b] such that exists for every and (1) converges for some (2) converges uniformly on [a,b]. Prove that converges uniformly on [a,b].Show how how this result may be used to weaken that hypothesis of 9.3I. [Hint: For write Apply 7.7A to obtain Theorem 9.3I If ( for each ) for each , if is continuous on [a,b], if converges on [a,b] to , and if converges uniformly on [a,b] to g, then . That is, --- We use the book Methods of Real Analysis by Richard Goldberg

tarea de clase

(See attached file for full problem description with equations) --- 1.- Let , . Does is uniformly converge on (-1,1)? --- We use the book Methods of Real Analysis by Richard Goldberg