# Uniform convergence of functions

Consider the sequence $\{f_n\}$ defined by $f_n(x) = \frac{nx}{ 1 + nx}$ , for $x ? 0$.

a) Find $f(x) = \lim _{n?? }f_n(x).$
b) Show that for $a > 0$, $\{f_n\}$ converges uniformly to $f$ on $[a,?)$.
c) Show that $\{f_n\}$ does not converge uniformly to $f$ on $[0,?).$

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