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(a) Suppose we have a function that is represented by a power series, f(x) = Σa," and we are told ag = -2, 8=0 7 a₁ = 0,02 = 2,93=5, a4 = -1, and as = 4, evaluate f" (0). (b) Suppose we have a function that is represented by a power series, g(x)=b". Write out the degree four Taylor polynomial centered at 0 for In(1+x)g(x). n=0 (c) Consider the differential equation, y' + In(1+r)y= cos(x) Suppose that we have a solution, y(x) = ena", represented by a Maclaurin series with nonzero radius of convergence, which also satisfies y(0) = 6. Determine C₁, C2, C3, and ca. N=0

(a) Suppose we have a function that is represented by a power series, f(x) = Σa," and we are told ag = -2, 8=0 7 a₁ = 0,02 = 2,93=5, a4 = -1, and as = 4, evaluate f" (0). (b) Suppose we have a function that is represented by a power series, g(x)=b". Write out the degree four Taylor polynomial centered at 0 for In(1+x)g(x). n=0 (c) Consider the differential equation, y' + In(1+r)y= cos(x) Suppose that we have a solution, y(x) = ena", represented by a Maclaurin series with nonzero radius of convergence, which also satisfies y(0) = 6. Determine C₁, C2, C3, and ca. N=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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(a) Suppose we have a function that is represented by a power series, f(x) = Σa," and we are told ag = -2, n=0 7 a₁ = 0,02 = 2,03=5, a4 = -1, and as = 4, evaluate f" (0). (b) Suppose we have a function that is represented by a power series, g(x)=b". Write out the degree four Taylor polynomial centered at 0 for In(1+x)g(x). n=0 (c) Consider the differential equation, y' + In(1+r)y= cos(x) Suppose that we have a solution, y(x) = ena", represented by a Maclaurin series with nonzero radius of convergence, which also satisfies y(0) = 6. Determine C₁, C2, C3, and ca. n=0
Transcribed Image Text:(a) Suppose we have a function that is represented by a power series, f(x) = Σa," and we are told ag = -2, n=0 7 a₁ = 0,02 = 2,03=5, a4 = -1, and as = 4, evaluate f" (0). (b) Suppose we have a function that is represented by a power series, g(x)=b". Write out the degree four Taylor polynomial centered at 0 for In(1+x)g(x). n=0 (c) Consider the differential equation, y' + In(1+r)y= cos(x) Suppose that we have a solution, y(x) = ena", represented by a Maclaurin series with nonzero radius of convergence, which also satisfies y(0) = 6. Determine C₁, C2, C3, and ca. n=0
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