Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Corollary 4.19: Taylor's theorem with Landau symbol
Let [a, b] CR be an interval with a ≤ b, let x, y ≤ (a,b), and let ƒ €
Cn+1([a, b]). Then
n
f(y) = f(¹)(x) (y − x)k + O(\y − x\”+1).
k!
k=0
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Transcribed Image Text:Corollary 4.19: Taylor's theorem with Landau symbol Let [a, b] CR be an interval with a ≤ b, let x, y ≤ (a,b), and let ƒ € Cn+1([a, b]). Then n f(y) = f(¹)(x) (y − x)k + O(\y − x\”+1). k! k=0
Can Taylor's theorem with Landau symbol (Corollary 4.19) be applied to the function
f: R. R, f(x) = sin(x²),
to find coefficients Yo,Y₁,Y2ER such that
holds for y=(-1,1)? If so, what is the sum
O
O
a. r=0
b. r=1
O c. r=2
O d. r=3
e. r=4
f(y) = y + y₁y+ 2y² + O(|y|³)
O f.
O g.
r=4π
Oh. r=8π
O i. The theorem cannot be applied in this context.
r=2π
r = 10 + 1₁ +12?
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Transcribed Image Text:Can Taylor's theorem with Landau symbol (Corollary 4.19) be applied to the function f: R. R, f(x) = sin(x²), to find coefficients Yo,Y₁,Y2ER such that holds for y=(-1,1)? If so, what is the sum O O a. r=0 b. r=1 O c. r=2 O d. r=3 e. r=4 f(y) = y + y₁y+ 2y² + O(|y|³) O f. O g. r=4π Oh. r=8π O i. The theorem cannot be applied in this context. r=2π r = 10 + 1₁ +12?
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Step 1

To find- Can Taylor's Theorem with landau symbol (Corollary 4.19) be applied to the function f :   fx = sinx2, to find thee coefficients γ0, γ1, γ2   such that fy = γ0 + γ1y + γ2y2 + Oy3 holds for y  -1, 1? If so, what is the sum r = γ0 + γ1 + γ2?

Advanced Math homework question answer, step 1, image 1

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