2. (Taylor series/polynomials) Find the Taylor series or polynomials generated by the following functions: i. f(x)=√√, centred at x = 4, of order 3 ii. f(x)cosh x ex + e-x 2 centred at x=0 iii. f(x) = cos(2x+/2), centred at x = π/4 iv. f(x) = cos 5x2, centred at x = 0. For this and subsequent questions you may use the formula for a frequently used Taylor series. v. f(x) = x tan¹ x², centred at x = 0 1 vi. f(x)= === centred at x = 0, of order 4
2. (Taylor series/polynomials) Find the Taylor series or polynomials generated by the following functions: i. f(x)=√√, centred at x = 4, of order 3 ii. f(x)cosh x ex + e-x 2 centred at x=0 iii. f(x) = cos(2x+/2), centred at x = π/4 iv. f(x) = cos 5x2, centred at x = 0. For this and subsequent questions you may use the formula for a frequently used Taylor series. v. f(x) = x tan¹ x², centred at x = 0 1 vi. f(x)= === centred at x = 0, of order 4
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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Transcribed Image Text:2. (Taylor series/polynomials) Find the Taylor series or polynomials generated by the following functions:
i. f(x)=√√, centred at x = 4, of order 3
ii. f(x)cosh x
ex + e-x
2
centred at x=0
iii. f(x) = cos(2x+/2), centred at x = π/4
iv. f(x) = cos 5x2, centred at x = 0. For this and subsequent questions you may use the formula for a frequently
used Taylor series.
v. f(x) = x tan¹ x², centred at x = 0
1
vi. f(x)=
===
centred at x = 0, of order 4
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