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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

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

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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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:
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