Question

24.2 For x ∈ [0, [infinity]), let fn(x) = x n . (a) Find f(x) = lim fn(x). (b) Determine whether fn → f uniformly on [0, 1]. (c) Determine whether fn → f uniformly on [0, [infinity])

Answer 1

a) Please Refer to the attachment below for answer and explanation.

b) Converges uniformly

c) Does not converges uniformly

Explanation:

Please Refer to the attachment below for answer and explanation.