(a) given, f(n) = {₁ 42 1-2n ^ [-3,1] ^ (1,7)

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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*) (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
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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