The set of all points of discontinuity of

Jazmin Strong

Jazmin Strong

Answered question

2022-04-11

The set of all points of discontinuity of the function f(x)=limnsin2n(πx2)

Answer & Explanation

tralhavahr9c

tralhavahr9c

Beginner2022-04-12Added 16 answers

Note that your limit is 0 whenever
|sin(πx2)|<1
and 1 if sin(πx2)=±1
So you have discontinuities whenever
sin(πx2)=±1
well this occurs whenever
πx2=πk
for any integer k. Or when
x=2k
an even integer. These are the points of discontinuity, since your function is
f(x)=(1,x=2k  kZ),(0, otherwise):

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