(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a sequence of continuous functions [tex]f_n: R \rightarrow R[/tex] such that [tex]lim_{x \rightarrow 0}lim_{n \rightarrow \infty}f_n(x) [/tex] and [tex]lim_{n \rightarrow \infty}lim_{x \rightarrow 0}f_n(x) [/tex] exist and are unequal.

2. Relevant equations

N/A

3. The attempt at a solution

I think I need a sequence of continuous functions that has a limit function which is continuous at zero but discontinuous at some other point. In that case, the sequence of functions will not be uniformly convergent and we will not have these limits equal. But I dont know what function can fulfill this criteria.

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# Interchange of limit operations

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