Tutorial Exercise Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R₂(x)→ 0.] Find the associated radius of convergence R. f(x) = 9/x, a-3 Step 1 The Taylor series formula is F(4) (a) (x - a)¹ + f(a) + f'(a)(x − a) + f(a)(x-a)² + (a)(x − a)³ +- 41 ✓ 2✔ |-6✔ -6 The function /(x) = can also be written as f(x) = (9), which has derivatives f'(x) = (9)- -, f"(x)= (9) f(x)= (9)- 2 4 24✔ 24 (4)(x)= (9) 5 Step 2 With a = -3, f(-3)= (9) „Ox Ox f"(-3) (9) „OX, f(-3)= (9)- and (4) (-3) (9) f'(-3)= (9)- 34 and
Tutorial Exercise Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R₂(x)→ 0.] Find the associated radius of convergence R. f(x) = 9/x, a-3 Step 1 The Taylor series formula is F(4) (a) (x - a)¹ + f(a) + f'(a)(x − a) + f(a)(x-a)² + (a)(x − a)³ +- 41 ✓ 2✔ |-6✔ -6 The function /(x) = can also be written as f(x) = (9), which has derivatives f'(x) = (9)- -, f"(x)= (9) f(x)= (9)- 2 4 24✔ 24 (4)(x)= (9) 5 Step 2 With a = -3, f(-3)= (9) „Ox Ox f"(-3) (9) „OX, f(-3)= (9)- and (4) (-3) (9) f'(-3)= (9)- 34 and
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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![Tutorial Exercise
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) → 0.] Find the associated radius of convergence R.
f(x) = 9/x, a-3
Step 1
The Taylor series formula is
f(a) + f'(a)(x − a) + f(a)(x − a)² + f(a)(x − a)³ +.
ƒ(4)(a) (x-a)4
2!
3!
4!
|-1 ✔
2✔
-6
The function f(x) = can also be written as f(x) = (9), which has derivatives ƒ'(x) = (9)-
f"(x)= (9)
f"(x)= (9)-
3
24
24
f(4)(x) = (9)
Step 2
X
With a = -3, f(-3)= (9).
f'(-3) (9)-
X
32
f"(-3) = (9)
X
33
f"(-3) = (9)-
34, and f(4) (-3) = (9)
Submit Skip (you cannot come back)
35
and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F671be518-f9e6-4df9-9304-33791fefeccb%2F3bf3f4a3-09c3-4936-8a46-4867a6701a01%2Fx9tcg8k_processed.png&w=3840&q=75)
Transcribed Image Text:Tutorial Exercise
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) → 0.] Find the associated radius of convergence R.
f(x) = 9/x, a-3
Step 1
The Taylor series formula is
f(a) + f'(a)(x − a) + f(a)(x − a)² + f(a)(x − a)³ +.
ƒ(4)(a) (x-a)4
2!
3!
4!
|-1 ✔
2✔
-6
The function f(x) = can also be written as f(x) = (9), which has derivatives ƒ'(x) = (9)-
f"(x)= (9)
f"(x)= (9)-
3
24
24
f(4)(x) = (9)
Step 2
X
With a = -3, f(-3)= (9).
f'(-3) (9)-
X
32
f"(-3) = (9)
X
33
f"(-3) = (9)-
34, and f(4) (-3) = (9)
Submit Skip (you cannot come back)
35
and
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