Problem 0.2 (centered at x = 0 unless specified): Subparts: = (1) f(x) (2) f(x) 1+x (3) f(x) 1 (1-a (4) f(x) 1 (1+x)³ (5) f(x) = e+e-x = = 1 4-x X = Find the Taylor series of the following functions (6) f(x) = x³ cos x (7) f(x) = ln(1 + x²) (8) f(x) = tan¯¹(x³) (9) f(x) = ln x centered at x = = 1 (10) f(x) = x5 - 3x + 17

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 0.2
(centered at x = 0 unless specified):
Subparts:
=
(1) f(x)
(2) f(x)
(3) f(x)
1
(1-x
1
(4) f(x)
(1+x)³
(5) f(x) = ex +e¯x
=
=
1
4-x
X
=
Find the Taylor series of the following functions
1+x
(6) f(x) = x³ cos x
(7) f(x) = ln(1 + x²)
(8) f(x) = tan¯¹(x³)
(9) f(x) = ln x centered at x = = 1
(10) f(x) = x5 - 3x + 17
Transcribed Image Text:Problem 0.2 (centered at x = 0 unless specified): Subparts: = (1) f(x) (2) f(x) (3) f(x) 1 (1-x 1 (4) f(x) (1+x)³ (5) f(x) = ex +e¯x = = 1 4-x X = Find the Taylor series of the following functions 1+x (6) f(x) = x³ cos x (7) f(x) = ln(1 + x²) (8) f(x) = tan¯¹(x³) (9) f(x) = ln x centered at x = = 1 (10) f(x) = x5 - 3x + 17
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