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Suppose T₁(x) 6-7x + 4x² - 5x³ +8x² is the degree 4 Taylor polynomial centered at x = 0 for a certain function f. Use T4 to estimate the value of f(0.1). 1. f(0.1) 5.2358 2. f(0.1) 5.5358 3. f(0.1) 5.6358 4. f(0.1) 5.4358 5. f(0.1) 5.3358 1. 002 Find the Taylor series centered at x = 0 for f(x) cos(4x). 2. 4. n=0 ∞ 3. Σ n=0 5. n=0 n 001 8 = n=1 8 6. Σ n=0 (-1)¹42n n! 8 4n (-1) 42n (2n)! (-1) ¹4²n (2n)! (2n)! 4n (2n)! xn x²n = (-1) 42n n! xn Xn x2n x2n 003 Find a power series representation centered at the origin for the function ∞ 1. Σ n=0 ∞ ∞ 2. Σ (-1)". n=0 ƒ(x) ∞ 6. Σ (n + 1)(n+2) 2.2n+3 3. Σ(-1) + 2n+2 n=0 8 n+1 5. Σ 2n+2 n=0 n=0 = (2 + x)-³. (n + 1)(n+2) 22n+3 ∞ 4. Σ (−1)n (n + 1)(n + 2) 2n+3 n=0 n+1 2.2n+2 xn xn Xn xn 004 Find the degree 2 Taylor polynomial of f centered at x = 2 when f(x) = 5x ln x. 5 1. 10 ln2+5ln 2(x − 2) + (x - 2)² 1 2. 10+5(ln 2+1)(x − 2) + - 5 (x − 2)² 5 3. 10ln2+5(ln2+1)(x − 2) + 6. 10+5 ln 2(x - 2) + 5 4. 10+2 ln 5(x-2) + (x - 2)² 5 5. 10 ln2+5(ln 2+1)(x − 2) + (x − 2)² 5 + ₂(x - 2)² (x − 2)²

Suppose T₁(x) 6-7x + 4x² - 5x³ +8x² is the degree 4 Taylor polynomial centered at x = 0 for a certain function f. Use T4 to estimate the value of f(0.1). 1. f(0.1) 5.2358 2. f(0.1) 5.5358 3. f(0.1) 5.6358 4. f(0.1) 5.4358 5. f(0.1) 5.3358 1. 002 Find the Taylor series centered at x = 0 for f(x) cos(4x). 2. 4. n=0 ∞ 3. Σ n=0 5. n=0 n 001 8 = n=1 8 6. Σ n=0 (-1)¹42n n! 8 4n (-1) 42n (2n)! (-1) ¹4²n (2n)! (2n)! 4n (2n)! xn x²n = (-1) 42n n! xn Xn x2n x2n 003 Find a power series representation centered at the origin for the function ∞ 1. Σ n=0 ∞ ∞ 2. Σ (-1)". n=0 ƒ(x) ∞ 6. Σ (n + 1)(n+2) 2.2n+3 3. Σ(-1) + 2n+2 n=0 8 n+1 5. Σ 2n+2 n=0 n=0 = (2 + x)-³. (n + 1)(n+2) 22n+3 ∞ 4. Σ (−1)n (n + 1)(n + 2) 2n+3 n=0 n+1 2.2n+2 xn xn Xn xn 004 Find the degree 2 Taylor polynomial of f centered at x = 2 when f(x) = 5x ln x. 5 1. 10 ln2+5ln 2(x − 2) + (x - 2)² 1 2. 10+5(ln 2+1)(x − 2) + - 5 (x − 2)² 5 3. 10ln2+5(ln2+1)(x − 2) + 6. 10+5 ln 2(x - 2) + 5 4. 10+2 ln 5(x-2) + (x - 2)² 5 5. 10 ln2+5(ln 2+1)(x − 2) + (x − 2)² 5 + ₂(x - 2)² (x − 2)²

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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Suppose T₁(x) 6-7x + 4x² - 5x³ +8x4 is the degree 4 Taylor polynomial centered at X 0 for a certain function f. Use T4 to estimate the value of f(0.1). 1. f(0.1) 5.2358 2. f(0.1) 5.5358 3. f(0.1) 5.6358 4. f(0.1)≈ 5.4358 5. f(0.1) 5.3358 1. 001 002 Find the Taylor series centered at x = 0 for f(x) cos(4x). 2. Σ IM8 IM8 IM8 IM8 IM8 IM8 = 3. Σ 6. (-1) 4²n n! (−1)n 42n (2n)! (-1) ¹4²n (2n)! 4n 4. Σ (2n)! 4n 5. Σ (2n)! Xn x ²n (−1)n 4²n n! = xn x²n x²n 003 Find a power series representation centered at the origin for the function f(x) = (2+x) −³. 1. ∞ n=0 ∞ 2. Σ (−1)n (n + 1)(n + 2) 2. 2n+3 n=0 ∞ 3. Σ (-1) n=0 ∞ 4. Σ (-1)" n=0 ∞ 5. Σ (n + 1)(n+2) 2.2n+3 1. 2. 3. n=0 ∞ 6. Σ n=0 n+ 1 2n+2 n+ 1 2n+2 xn (n + 1)(n+2) 2n+3 n+1 2.2n+2 Xn xn xn f(x) Xn 004 Find the degree 2 Taylor polynomial of f centered at x = 2 when xn = 5x ln x. 5 10ln2+5ln 2(x − 2) + (x − 2)² 10+5(ln2+1)(x − 2) + - 5 (x − - 5 10 ln2+5(ln 2+1)(x − 2) + 5 4. 10+2ln5(x - 2) + (x - 2)² 2)² 5 6. 10+5 ln 2(x − 2) + (x - 2)² (x − 2)² 5 5. 10 In 2+5(ln 2+ 1)(x − 2) + − (x − 2)²
Transcribed Image Text:Suppose T₁(x) 6-7x + 4x² - 5x³ +8x4 is the degree 4 Taylor polynomial centered at X 0 for a certain function f. Use T4 to estimate the value of f(0.1). 1. f(0.1) 5.2358 2. f(0.1) 5.5358 3. f(0.1) 5.6358 4. f(0.1)≈ 5.4358 5. f(0.1) 5.3358 1. 001 002 Find the Taylor series centered at x = 0 for f(x) cos(4x). 2. Σ IM8 IM8 IM8 IM8 IM8 IM8 = 3. Σ 6. (-1) 4²n n! (−1)n 42n (2n)! (-1) ¹4²n (2n)! 4n 4. Σ (2n)! 4n 5. Σ (2n)! Xn x ²n (−1)n 4²n n! = xn x²n x²n 003 Find a power series representation centered at the origin for the function f(x) = (2+x) −³. 1. ∞ n=0 ∞ 2. Σ (−1)n (n + 1)(n + 2) 2. 2n+3 n=0 ∞ 3. Σ (-1) n=0 ∞ 4. Σ (-1)" n=0 ∞ 5. Σ (n + 1)(n+2) 2.2n+3 1. 2. 3. n=0 ∞ 6. Σ n=0 n+ 1 2n+2 n+ 1 2n+2 xn (n + 1)(n+2) 2n+3 n+1 2.2n+2 Xn xn xn f(x) Xn 004 Find the degree 2 Taylor polynomial of f centered at x = 2 when xn = 5x ln x. 5 10ln2+5ln 2(x − 2) + (x − 2)² 10+5(ln2+1)(x − 2) + - 5 (x − - 5 10 ln2+5(ln 2+1)(x − 2) + 5 4. 10+2ln5(x - 2) + (x - 2)² 2)² 5 6. 10+5 ln 2(x − 2) + (x - 2)² (x − 2)² 5 5. 10 In 2+5(ln 2+ 1)(x − 2) + − (x − 2)²
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