(a) Show for all x Є R, the sum Σx=-17/2 COS (2) converges uniformly. (b) Show for all x = R, the sum Σx=-173 sin (22) converges uniformly. (c) Find a relationship between 2 c f: RR defined by COS n³ (2) and sin (2) and use this to show is differentiable. f(x) = Στ n=1 X COS

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) Show for all x = R, the sum
(b) Show for all x = R, the sum Σ
(c) Find a relationship between
ƒ : R → R defined by
n
=172 COS (22) converges uniformly.
x 1 1/3 sin (2) converges uniformly.
COS
n3
(22) and 13 sin (22) and use this to show
n3
is differentiable.
f(x)
=
n=1
1
n²
COS
()
Transcribed Image Text:(a) Show for all x = R, the sum (b) Show for all x = R, the sum Σ (c) Find a relationship between ƒ : R → R defined by n =172 COS (22) converges uniformly. x 1 1/3 sin (2) converges uniformly. COS n3 (22) and 13 sin (22) and use this to show n3 is differentiable. f(x) = n=1 1 n² COS ()
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