(a) Determine whether or not each of the following functions is uniformly continuous: i. f:Qn(-2,2) →R defined by f(x) = 4x³ – 2x² +8, V.x E Qn(-2,2). ii. g: E→R defined by 5, g(x) = x= 1 3, х€Е-{1} where E = {0}U{ :neN}.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3.
(a) Determine whether or not each of the following functions is uniformly
continuous:
i. f:Qn(-2,2) → R defined by
f(x) = 4x – 2x2 +8, Vx E Qn(-2,2).
ii. g: E→R defined by
{
S 5,
3, х€E-{1}
x = 1
g(x) =
%3D
where E = {0}U{:n eN}.
(b) Consider the function h: (0,27) → R defined by
{
-1, x€Qn (0,2n)
2, x€ Q°n (0, 27)
h(x) =
Prove that h is nowhere continuous on (0,2n).
Transcribed Image Text:3. (a) Determine whether or not each of the following functions is uniformly continuous: i. f:Qn(-2,2) → R defined by f(x) = 4x – 2x2 +8, Vx E Qn(-2,2). ii. g: E→R defined by { S 5, 3, х€E-{1} x = 1 g(x) = %3D where E = {0}U{:n eN}. (b) Consider the function h: (0,27) → R defined by { -1, x€Qn (0,2n) 2, x€ Q°n (0, 27) h(x) = Prove that h is nowhere continuous on (0,2n).
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