In Example 2.4.1, show that fn(x) converges to f(x) pointwise on [0, 1]. (We have seen the convergence at x =

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Text: Example 2.4.1. For rE 0,1] and positive integer n, let f,(r) = z”. Then lim fa(r) = f(r),, where 0if0

In Example 2.4.1, show that fn(x) converges to f(x) pointwise on [0, 1]. (We have seen the convergence at x = 0, 1.) For x ∈ [0, 1] and positive integer n, let fn(x) = xn. Then limn→∞ fn(x) = f(x),, where f(x) = 0 if 0 ≤ x < 1, 1 if x = 1. Ts example shows that the pointwise limit of a sequence of continuous functions need not be continuous. Transcribed Image Text: Question 5. In Example 2.4.1, show that fn(r) converges to f(x) pointwise on [0, 1]. (We have seen the convergence at r = 0, 1.) Transcribed Image Text: Example 2.4.1. For rE 0,1] and positive integer n, let f,(r) = z". Then lim fa(r) = f(r),, where 0if0

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