3. Find the pointwise limit of the sequence of functions defined on R by the followingand determine whether or not the convergence is uniform.(i) f(x) = si, a [0, π].(ii) f(x) = (cos Tx)2n for all z E R.(iii) fn(x) = n²x(1-x)", z = [0, 1].

To find the pointwise limit of the sequence of functions and determine whether convergence is…

Answered: 3. Find the pointwise limit of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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. (i) f(x)=sin, x € [0, π]. (ii) f(x) = (cos Tx)2n for all z E R. (iii) fn(x) = n²x(1-x)", z = [0, 1].