4х - 6 2. Let f(x) 1- (2х-3)3" a. Find the Taylor series representation for f about x = 1.5 that is valid for all x e (1,2). +00 1 Hint: Use the equation 1-t E", where te (-1,1), to find the Taylor series representation for n=0 1 about x = 1.5. Then, use this series to find the desired series representation for f. 1- (2x – 3)3 b. Use the result in item 2(a) to find the 4th degree Taylor polynomial of f about 1.5. c. Use the result in item 2(b) to approximate f(1.55). Express your answer in decimal form.
4х - 6 2. Let f(x) 1- (2х-3)3" a. Find the Taylor series representation for f about x = 1.5 that is valid for all x e (1,2). +00 1 Hint: Use the equation 1-t E", where te (-1,1), to find the Taylor series representation for n=0 1 about x = 1.5. Then, use this series to find the desired series representation for f. 1- (2x – 3)3 b. Use the result in item 2(a) to find the 4th degree Taylor polynomial of f about 1.5. c. Use the result in item 2(b) to approximate f(1.55). Express your answer in decimal form.
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
![4x – 6
2. Let f(x)
1- (2x – 3)3
a. Find the Taylor series representation for f about x = 1.5 that is valid for all x e (1,2).
+00
1
Hint: Use the equation
E", where te (-1,1), to find the Taylor series representation for
1-t
n=0
1
about x = 1.5. Then, use this series to find the desired series representation for f.
1- (2x – 3)3
b. Use the result in item 2(a) to find the 4th degree Taylor polynomial of f about 1.5.
c. Use the result in item 2(b) to approximate f(1.55). Express your answer in decimal form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2313883-0453-46f3-9caf-487535e9bad7%2F6f46c965-6d96-4edc-9a86-92d8840bcb49%2Fiu3xq8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4x – 6
2. Let f(x)
1- (2x – 3)3
a. Find the Taylor series representation for f about x = 1.5 that is valid for all x e (1,2).
+00
1
Hint: Use the equation
E", where te (-1,1), to find the Taylor series representation for
1-t
n=0
1
about x = 1.5. Then, use this series to find the desired series representation for f.
1- (2x – 3)3
b. Use the result in item 2(a) to find the 4th degree Taylor polynomial of f about 1.5.
c. Use the result in item 2(b) to approximate f(1.55). Express your answer in decimal form.
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