# Michigan State University Sequences of Functions Questions

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these questions all based on theorem and definition. doesnot need plenty of time to do it.

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Problem 6 Let ______ and _____ be sequences of bounded functions on ICR that converge uniformly

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n=1
Problem 6
het
nyo and
of guyo
be sequences
of
bounded funcbons
I CR that converge uniformly
f and g. Prove that fut gr,
fn-gn, and fregn also converge uniformly.
on т
to

Problem
fn: IR
R.
be
ne N V
het
Ini I (0,to)
sequences of functions
that uniformly converge
Prove
that
as
ho.
disprove
Problem 8 E
n h
n=
het
f() = 3 cos (nx),
f
is differentiable the interval
CE[0, 2u]
Prove that
on ท
[0,
20]
Problem 9
5
Prove that
Ź tan a mi)
n=1
[
informly
[- [ ]
um
on ท
Converges

Problem 10
sW
an
x
Consider
Ž
(con
(2n)!
n=o
series
Converse
on
xan
sum
noo
Prove
that the
pointwise
R and denote the
f(x)
S (1)”
(24)!!!
Without computing f explicitely,
show that
f
twice differential
and f”=-f.
IS

attachment

Tags:
Ratio test

converge uniformly

Sequences of functions

Defined on the interval

Weierstrass M test

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