For each n ∈ N, let f_n(x) = a_nx + b_n where a_n,b_n are sequences of...

For each n ∈ N, let f_n(x) = a_nx + b_n where a_n,b_n are sequences of real numbers. Prove that if f_n → f on [0,1] where f is a function on [0,1], then the convergence is necessarily uniform.

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Expert Solution

First we find the function f by using the pointwise convergence .then we proceed for uniform convergence of sequence fn.

Colby Messinger answered 9 months ago

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