(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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc88a61a8-930a-4496-81c3-aab24a173799%2Fe3663810-4165-4890-9afa-d5ed30573db9%2Fwunq5j4_processed.jpeg&w=3840&q=75)
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!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc88a61a8-930a-4496-81c3-aab24a173799%2Fe3663810-4165-4890-9afa-d5ed30573db9%2Fj3i1d8mj_processed.jpeg&w=3840&q=75)
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!
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)