2. (a) Prove that 00 (_l)k+l x=2L k sinkx k=1 pointwise on (-1f, 1f) and uniformly on...
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2.
(a) Prove that 00 (_l)k+l x=2L k sinkx k=1 pointwise on (-1f, 1f) and uniformly on any [a, b] c (-1f, 1f).
(b) Prove that Ixl = ~ _ ~ ~ cos(2k - l)x 2 1f~ (2k-1)2 uniformly on [-1f, 1f].
(c) Find a value for 00 1 t;(2k-1)2'
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