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Consider the sequence of functions: $$ f_n(x) = \frac{n}{x+n}. $$ Step 1: Find the pointwise limit on $[0, k]$, $k>0$ For fixed $x \in [0, k]$, $$ \lim_{n \to \infty} f_n(x) = \lim_{n \to \infty} \frac{n}{x+n} = \lim_{n \to \infty} \frac{1}{1 + \frac{x}{n}} = 1. $$ So, the pointwise limit function is $$ f(x) = 1 \quad \text{for } x \in [0, k]. _______ ________ _______ _________ __________ ________ __________ __________ __________ _________ ___ ____.
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