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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

2 votes
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Sequence tending to modulus function

I am looking for a sequence of smooth functions $f_n: \mathbb R^2 \rightarrow \mathbb R$such that the 1.) the nodal set of $f_n$, i.e. $N_n:=f_n^{-1}(0)$ converges to the graph of the absolute value …