Problem 4 Let An (0) = 1 1+ (x/n)² Part (a): Find the limit function f of the sequence of functions (fr). This will just

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Problem 4 Let An 0 1 1 X N Part A Find The Limit Function F Of The Sequence Of Functions Fr This Will Just 1 (48.26 KiB) Viewed 24 times

Problem 4 Let An (0) = 1 1+ (x/n)² Part (a): Find the limit function f of the sequence of functions (fr). This will just be the pointwise limit, f(x) = lim f(x). (Think: Hold & constant while taking the limit as n → ∞.) n+00 Part (b): Plot f1, f2, and f5 along with f on the interval [0, 1]. Part (c): Prove the sequence of functions (fr) converges uniformly on the interval [0, 1] to the function f. Hint: Find ||fn - fl|u over [0, 1]. Part (d): Does the sequence (fr) converge to f uniformly on the entire real number line R? Hint: This time, to find ||fn - fu think of the value of fn (x) f(x) for a large number (assuming n is fixed).