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

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

Advanced Engineering Mathematics
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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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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