. Find the pointwise limit of the sequence of functions defined on R by the following and determine whether or not the convergence is uniform. (i) ƒn(x) = sinn², x ¤ [0, π]. (ii) f(x) = (cos x)2n for all x € R. (iii) fn(x) = n²x(1-x)", x € [0, 1].

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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converges pointwise on [0, 1]. Argue that the convergence is not uniform.
3. Find the pointwise limit of the sequence of functions defined on R by the following
and determine whether or not the convergence is uniform.
sin na
(i) fn(r)
VE [0, π].
(ii) f(x) = (COS TT)2n for all r ER.
(iii) fn(x) = n²x(1-x)", x € [0, 1].
Transcribed Image Text:G www.google.com 20 Read aloud Gmail YouTube 1 Maps + e 1 G7 G7FX Workshop Pla... of 1 > Thursday class (Tut... converges pointwise on [0, 1]. Argue that the convergence is not uniform. 3. Find the pointwise limit of the sequence of functions defined on R by the following and determine whether or not the convergence is uniform. sin na (i) fn(r) VE [0, π]. (ii) f(x) = (COS TT)2n for all r ER. (iii) fn(x) = n²x(1-x)", x € [0, 1].
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