Read the example in the photos, concerning the limit of the sequence (1/n). For this example: give (with explanation) three values of N that "work" with the definition for ε = 1/10, and three values of N for ε = 1/100.
Read the example in the photos, concerning the limit of the sequence (1/n). For this example: give (with explanation) three values of N that "work" with the definition for ε = 1/10, and three values of N for ε = 1/100.
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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Read the example in the photos, concerning the limit of the sequence (1/n). For this example: give (with explanation) three values of N that "work" with the definition for ε = 1/10, and three values of N for ε = 1/100.
![Exampler Lim /n =0,
then
You
nico
Since VESO, if we take N= 1/₂
n>N>0 =>0<<< 1/1 = 1/₁2 = E
So [n>N] → [1½-01<E]
for this N.
35
may
be wondering why this definition seems so complicated. The
following helps show why many simpler alternatives faile](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67d7419-2a0a-426e-a502-74f41ba49d7f%2Fbbececdd-7f04-4ae2-956c-476d97270146%2F87b7b7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exampler Lim /n =0,
then
You
nico
Since VESO, if we take N= 1/₂
n>N>0 =>0<<< 1/1 = 1/₁2 = E
So [n>N] → [1½-01<E]
for this N.
35
may
be wondering why this definition seems so complicated. The
following helps show why many simpler alternatives faile
Transcribed Image Text:Antiexample: Consider (Sn)neN
Although Sn is
1 infinitely many times,
times.
it is also -1 infinitely
and it doesn't seem
gets closer
Indeed, if E=1
=
many
accurate to
and closer" to either.
·((-1)^) = (1, -1, 1,-1,...).
whenever n is odd.
(or
say
that it
smaller value), then
15₂-11 > E
any
That is, Isn-11 is 271 when n is odd
when n is even.)
(and O
No matter how big N is, there will always be odd numbers
bigger.
that are
This shows that LimSn #1, since
ε =1 has
the needed condition.
no
N satisfying
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