I finished exploring a family of functions(adsbygoogle = window.adsbygoogle || []).push({});

f_{k}(x) = {x^{k}sin(1/x) for x≠0

{0 for x=0

for an assignment in my Analysis course, and I'm supposed to determine the highest order derivative that exists and whether or not it's continuous.

I've noticed a pattern:

k= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}

n= {0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...},

wherekis a positive integer, andnis the highest order derivative that exists.

I want to save some space on my page by generalizing these results as a sequence. Is this possible, and if so what's the sequence? Thanks.

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# Is a general sequence possible for the given data?

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