►h) fn(x)= ( 1+ ,x € R n
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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Can I have a detailed, step-by-step explanation for the following problem?
![1. Define in the usual notation, the pointwise convergence of a sequence of functions {fn(x)}1
on the domain DCR.
Find the pointwise limit function of the each of the following sequence of functions, defined
in the indicated limit.
sin(nx)
a) fn(x) =
", x ε R
n2
b) fa(") %3D пx(1- 2)", 2 € [0, 1]
c) fn(x) =
,x € [0, 0)
1+ nx
d) fn(x)= e¬n², x € R
sin(nx + 3)
Vn +1
e) fn(x) =
,x € R
f) fn(x)= n²x²,0 <x < 1
g) fn(x) =
n2
(x + n)?
-,x € R
h) fn(x) = ( 1+
,x ER](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e8bcb0d-46db-4931-99e9-9b266face003%2F0e8dcf3b-ba46-4ae1-bd22-49e768871720%2F4ym0e7_processed.png&w=3840&q=75)
Transcribed Image Text:1. Define in the usual notation, the pointwise convergence of a sequence of functions {fn(x)}1
on the domain DCR.
Find the pointwise limit function of the each of the following sequence of functions, defined
in the indicated limit.
sin(nx)
a) fn(x) =
", x ε R
n2
b) fa(") %3D пx(1- 2)", 2 € [0, 1]
c) fn(x) =
,x € [0, 0)
1+ nx
d) fn(x)= e¬n², x € R
sin(nx + 3)
Vn +1
e) fn(x) =
,x € R
f) fn(x)= n²x²,0 <x < 1
g) fn(x) =
n2
(x + n)?
-,x € R
h) fn(x) = ( 1+
,x ER
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