93.3

(See attached file for full problem description with proper equations) --- 9.3-3 Let . Use the result of exercise 4 of Section 9.1 to show that does not converge uniformly on [0,1], even though converges pointwise. ---

93.4

(See attached file for full problem description with proper equations) --- 9.3-4 Let . Show that converges uniformly to 0 on [0,1], but that does not converge (even) pointwise to 0 on [0,1 ---

93.5

(See attached file for full problem description with proper 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 ---

94.2

(See attached file for full problem description with equations) --- 9.4-2 Does the series converge uniformly on (Hint: Find the sum of the series for all x) --- We are using the book of Methods of Real Analysis by Richard Goldberg

94.5

(See attached file for full problem description with equations) --- 9.4-5 Show that the series is uniformly convergent on [0,A] for any A>0. Prove that --- We are using the book of Methods of Real Analysis by Richard Goldberg