Draw, in standard position, the angle whose measure is given: (4pi)/3

cooloicons62 2022-07-16 Answered
Draw, in standard position, the angle whose measure is given:
4 π 3
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Answers (2)

Alexia Hart
Answered 2022-07-17 Author has 19 answers
Jeffrey Jordon
Answered 2022-07-26 Author has 2581 answers

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I am strugling with this exercise:
Let f n ( t ) = sin ( n t ). Prove that f n 0 in L [ 0 , 2 π ]
The solution given to me reads:
Since the given space is the dual of L 1 [ 0 , 2 π ] : L [ 0 , 2 π ] = ( L 1 [ 0 , 2 π ] )
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That is straightforward since I can easily integrate sin(nt) over [a,b]and notice it converges to 0, but I don't understand why/ I am not convinced that it is enough to do so. I have read elsewhere that " a sequence of continuous functions on a metric space that converges pointwise on a dense subset need not converge pointwise on the full space.",
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