Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT
![*) (a) given, f(~) =
NOW,
(im f(n)
ngit
Hence,
(im f(n) = (im
"+1-
141-
1
r
=
T
n²nt [-3,1]
, " (1,7)
1-2n
at nal
=
lim
hot
(1-6)2
tim (1-2h+b)
hot
1.
42
1
lim ((-2^)
пян
lim
hyot
= 1-2.0 +0²
2 lim h + lim ²
hot
hyot
(1-2(1+5))
(im (-1-2h)
h 10+
(As, n+1-, hot
(since, n=1-h))
and
f(1) = 1²=1.
f(n) has jump discontinuity at nal,
i.e, 1st type of discontinuity.
(Note that, this discontinuity is not nemovable
discontinuity,
Cause,
at usa, f(u) hay nemovable discontinuity
(im f(u) = (im tru) & f(a)
it
nya-
nyat
and in this case, we can redefine the function
make, t(u) i continuary at nea
n=a.
to
But given f(n) at nal,
Ис
(im f(n) & lim f(n)
M (
Malt
Hence we can't redefine f(n) at nal
to
make f(n) i continuous at nal](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc52fbd7b-9adb-4e52-81b8-0bf956b4f8e7%2Fcc5a8f94-b1ef-4070-839b-fa3ccda2b38a%2Fnn0yakp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:*) (a) given, f(~) =
NOW,
(im f(n)
ngit
Hence,
(im f(n) = (im
"+1-
141-
1
r
=
T
n²nt [-3,1]
, " (1,7)
1-2n
at nal
=
lim
hot
(1-6)2
tim (1-2h+b)
hot
1.
42
1
lim ((-2^)
пян
lim
hyot
= 1-2.0 +0²
2 lim h + lim ²
hot
hyot
(1-2(1+5))
(im (-1-2h)
h 10+
(As, n+1-, hot
(since, n=1-h))
and
f(1) = 1²=1.
f(n) has jump discontinuity at nal,
i.e, 1st type of discontinuity.
(Note that, this discontinuity is not nemovable
discontinuity,
Cause,
at usa, f(u) hay nemovable discontinuity
(im f(u) = (im tru) & f(a)
it
nya-
nyat
and in this case, we can redefine the function
make, t(u) i continuary at nea
n=a.
to
But given f(n) at nal,
Ис
(im f(n) & lim f(n)
M (
Malt
Hence we can't redefine f(n) at nal
to
make f(n) i continuous at nal
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