3. Find Taylor's series for f(x) centered at the given point a, as well as the associated radius of convergence: a. f(x) = 2cos²x, a = л/2 b. f(x) = e3x, a = 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
icon
Related questions
Question
Solve problem 3 with explanation.
9 27
g. 4+3+-+
4 16
+...
h.
2 1 2 1 2
+ + + +
+
39
27 81 243 729
1
+...
3. Find Taylor's series for f(x) centered at the given point a, as well as the associated radius of convergence:
a. f(x) = 2 cos²x, a = π/2
b. f(x) = e³x, a = 1
4. Find MacLaurin's series (i) using the known function series (see slide 30 from the Lecture Notes or the next
page) or (ii) using the definition. Also find the associated radius of convergence of:
a.
f(x) = 2.e5x+2
b. f(x) = 2x³5x+2
c. f(x) = x. cos²x
d. f(x) = 5x
e. f(x) = xsin(x)
f. f(x) = (11-3x)2/3
5. Express the number as a ratio of integers:
Transcribed Image Text:9 27 g. 4+3+-+ 4 16 +... h. 2 1 2 1 2 + + + + + 39 27 81 243 729 1 +... 3. Find Taylor's series for f(x) centered at the given point a, as well as the associated radius of convergence: a. f(x) = 2 cos²x, a = π/2 b. f(x) = e³x, a = 1 4. Find MacLaurin's series (i) using the known function series (see slide 30 from the Lecture Notes or the next page) or (ii) using the definition. Also find the associated radius of convergence of: a. f(x) = 2.e5x+2 b. f(x) = 2x³5x+2 c. f(x) = x. cos²x d. f(x) = 5x e. f(x) = xsin(x) f. f(x) = (11-3x)2/3 5. Express the number as a ratio of integers:
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage