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Gzlac) = (-0.08333) (x-2)(x-3)(2-4) + (0-4)(2-1)LC-s)(x4) (-6-45)(x-1)(x-23(x-4) + (0.15686)x-1)(x-2XX-3) t => fg Cac) = 191.59y?-404.33y"+282.46y-62.971

Gzlac) = (-0.08333) (x-2)(x-3)(2-4) + (0-4)(2-1)LC-s)(x4) (-6-45)(x-1)(x-23(x-4) + (0.15686)x-1)(x-2XX-3) t => fg Cac) = 191.59y?-404.33y"+282.46y-62.971

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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Question 2b. I have this but am unsure how to get from one step to the next where the question mark is.

Draw View T Text Mode Lasso Select - Insert Space ork Io =1,C1=2,x2=3,13=4 26) f, (x) = (o.5) (x-2)(x-3)(x-4) (1-2) (1-3) (I-4) F(E) + (o-8) (I-1)l2-3)(x-4) (2-1) (2-3) (2-4) t l0-9) (x-1)(x-2)(c-4) (3-1)(3-2)13-4) Flai E le « + Lo941196) (x-n(x-2)2-3) JA O =| - 20 (4-1)(4-2)14-3) fglac) = (-0.08333)z-2)x-3)(2-4) + (0-4)(x-1)Lc-s)(x4) + (-6.45) (x-1)(x-2)(x-4) + (0.15686) (2x-1)(x-2X3) %3D 2 =) Fz Coc) = 19l.s9y-404.8 3 y+282.46y -62.971 %3D
Transcribed Image Text:Draw View T Text Mode Lasso Select - Insert Space ork Io =1,C1=2,x2=3,13=4 26) f, (x) = (o.5) (x-2)(x-3)(x-4) (1-2) (1-3) (I-4) F(E) + (o-8) (I-1)l2-3)(x-4) (2-1) (2-3) (2-4) t l0-9) (x-1)(x-2)(c-4) (3-1)(3-2)13-4) Flai E le « + Lo941196) (x-n(x-2)2-3) JA O =| - 20 (4-1)(4-2)14-3) fglac) = (-0.08333)z-2)x-3)(2-4) + (0-4)(x-1)Lc-s)(x4) + (-6.45) (x-1)(x-2)(x-4) + (0.15686) (2x-1)(x-2X3) %3D 2 =) Fz Coc) = 19l.s9y-404.8 3 y+282.46y -62.971 %3D
Emply inverse interpolation to determine the value of x that corresponds to f (x) = 0.85 for the following tabulated data generated with the function x? f(x) = 2 1+x2 1 | 2 3 4 5 f(x) 0.5 0.8 0.9 0.941176 0.961538 (a) Determine the correct value analytically. (b) Use cubic interpolation of x versus y or f (x). Compute the true percent relative error. (c) Use inverse interpolation with quadratic interpolation and the quadratic formula. Compute the true percent relative error. (d) Use inverse interpolation with cubic interpolation and bisection. Compute the true percent relative error. (e) Compare the results from (b), (c), and (d) and comment on your findings.
Transcribed Image Text:Emply inverse interpolation to determine the value of x that corresponds to f (x) = 0.85 for the following tabulated data generated with the function x? f(x) = 2 1+x2 1 | 2 3 4 5 f(x) 0.5 0.8 0.9 0.941176 0.961538 (a) Determine the correct value analytically. (b) Use cubic interpolation of x versus y or f (x). Compute the true percent relative error. (c) Use inverse interpolation with quadratic interpolation and the quadratic formula. Compute the true percent relative error. (d) Use inverse interpolation with cubic interpolation and bisection. Compute the true percent relative error. (e) Compare the results from (b), (c), and (d) and comment on your findings.
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