radius of convergence of the taylor series for (x2-2x+2)-1 about x-0

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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what is the radius of convergence of the taylor series for (x2-2x+2)-1 about x=0
(x2 – 2x + 2)-1
Concept
Radius ols convergence el Taylos series for (oe²-2<+3)+
about =o
is the radius odk the biggest cixele that
can be drsaun Anking (0,0) as the center of the circle
so that there be no amy
point inside the cirele
where (x?-2x+3)-1 is not analy tical.
We have,
つc2-2243
We know that denominator should nit be equal to zero.
?-2x+3 6
ー(-2)はJE2)-4x4メ3
solution of quadrdhie
equa tron]
2メ1
2土J4-42
2
2t J-8
つく そ
2
2 + 212 i
=)
2
Hence, (x²-?x+3) is not critical at
Hence,
(c?- 23c+3)? is not analy ticad at (1,-3)
and (1, z).
2
Since, pe?-2x+3)t isnot
analydrend at (1,-v)
Transcribed Image Text:what is the radius of convergence of the taylor series for (x2-2x+2)-1 about x=0 (x2 – 2x + 2)-1 Concept Radius ols convergence el Taylos series for (oe²-2<+3)+ about =o is the radius odk the biggest cixele that can be drsaun Anking (0,0) as the center of the circle so that there be no amy point inside the cirele where (x?-2x+3)-1 is not analy tical. We have, つc2-2243 We know that denominator should nit be equal to zero. ?-2x+3 6 ー(-2)はJE2)-4x4メ3 solution of quadrdhie equa tron] 2メ1 2土J4-42 2 2t J-8 つく そ 2 2 + 212 i =) 2 Hence, (x²-?x+3) is not critical at Hence, (c?- 23c+3)? is not analy ticad at (1,-3) and (1, z). 2 Since, pe?-2x+3)t isnot analydrend at (1,-v)
Hence, (x²-2x+3)? is not critical at
Hence, (oc?-2>+3) is not analy tical at (1,-52)
and (1, Jz).
2
Since, be?-23x+3)t isnot
analydread at (1,-)
and (ti vz). Thereboor, x'
these two points should
!A
-1
OU,0) 1
ー2
-1
not come inside the
-Jz
Circle drawn whose
ceters is (0,0).
-2
The larrgest circle will pess
though p(1,52) and 9 (1,-S)
as p(?, JZ) and o?,-v2) are equidistance frum ocoi0).
In right-engled DOAP,
Y= Ju*+(近)
Je42
Hence, the cororeet option is
D. J3
Canswer)
Transcribed Image Text:Hence, (x²-2x+3)? is not critical at Hence, (oc?-2>+3) is not analy tical at (1,-52) and (1, Jz). 2 Since, be?-23x+3)t isnot analydread at (1,-) and (ti vz). Thereboor, x' these two points should !A -1 OU,0) 1 ー2 -1 not come inside the -Jz Circle drawn whose ceters is (0,0). -2 The larrgest circle will pess though p(1,52) and 9 (1,-S) as p(?, JZ) and o?,-v2) are equidistance frum ocoi0). In right-engled DOAP, Y= Ju*+(近) Je42 Hence, the cororeet option is D. J3 Canswer)
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