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(v) Finally, determine the degree n Taylor polynomial, pn, centered at x = 0 for f. η 1. p(x) = e'(Σ(-1)* **14) 2k k! k=0 η 2. P(x) = e(Σ*t) k k=0 3. pn(x) = 5. pn(2) e 4. Pn(m) = e(Σ(-1)^2*wt) k k=0 = 4 4 η 1 (ΣΑ) k! k=0 e η (Σ) k=0

(v) Finally, determine the degree n Taylor polynomial, pn, centered at x = 0 for f. η 1. p(x) = e'(Σ(-1)* **14) 2k k! k=0 η 2. P(x) = e(Σ*t) k k=0 3. pn(x) = 5. pn(2) e 4. Pn(m) = e(Σ(-1)^2*wt) k k=0 = 4 4 η 1 (ΣΑ) k! k=0 e η (Σ) k=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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f(x) = e^(2x+4)

(part 5 of 5) (v) Finally, determine the degree n Taylor polynomial, pn, centered at x = 0 for f. 1. pn(2) = 2. pn(x) : = η et (Σ(-1)* k! 24 k=0 4 e (Σ) k=0 η 3. Pa(n) = e (ΣΗ**) 1 4 k! k=0 όλ η 5. P«(n) = e (Σ?) k=0 4) η 4. P(x) = e' (Σ(-1)* *r*) 24 : k=0
Transcribed Image Text:(part 5 of 5) (v) Finally, determine the degree n Taylor polynomial, pn, centered at x = 0 for f. 1. pn(2) = 2. pn(x) : = η et (Σ(-1)* k! 24 k=0 4 e (Σ) k=0 η 3. Pa(n) = e (ΣΗ**) 1 4 k! k=0 όλ η 5. P«(n) = e (Σ?) k=0 4) η 4. P(x) = e' (Σ(-1)* *r*) 24 : k=0
3. 1/7 f(n) (0) = 27e4 n! 4. —ƒ(¹) (0) 5. f() (0) = 1. p3(x) = e 2. p3(x) = (part 4 of 5) (iv) Determine the degree 3 Taylor polynomial, P3, centered at x 0 for f. = 3. p3(x) = e 6. p3(x) 2n n = 1 -4 5. p3(x) = е¯ -e4 n! 4 -4 4 (1 1+ 2x + 2x² + e¹(1+2x - 2x² e¹ (1 4. p3(x) = e¹(1 − 2x + 2x² -4 ¹(1 2x + 2x² (122:²³) 72³) 4 172³) col Acol 1 + 2x 2x² ² + 1/32²³) 4 e¹ (1 + 2x + 2x² + ²32³3) (part 3 of 5) (iii) Compute the value of f(n) (0). 1. 1- f(n) (0) = 2" . e4 2. 1-7 f(n) (0) = 2n Teln е n!
Transcribed Image Text:3. 1/7 f(n) (0) = 27e4 n! 4. —ƒ(¹) (0) 5. f() (0) = 1. p3(x) = e 2. p3(x) = (part 4 of 5) (iv) Determine the degree 3 Taylor polynomial, P3, centered at x 0 for f. = 3. p3(x) = e 6. p3(x) 2n n = 1 -4 5. p3(x) = е¯ -e4 n! 4 -4 4 (1 1+ 2x + 2x² + e¹(1+2x - 2x² e¹ (1 4. p3(x) = e¹(1 − 2x + 2x² -4 ¹(1 2x + 2x² (122:²³) 72³) 4 172³) col Acol 1 + 2x 2x² ² + 1/32²³) 4 e¹ (1 + 2x + 2x² + ²32³3) (part 3 of 5) (iii) Compute the value of f(n) (0). 1. 1- f(n) (0) = 2" . e4 2. 1-7 f(n) (0) = 2n Teln е n!
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