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MATH08013: Use an appropriate Taylor series to write a MATLAB function M-file that approximates 𝑓(π‘₯) = sin(2π‘₯): Maths Assignment, UCC, Ireland

University University College Cork (UCC)
Subject MATH08013: Maths Assignment

Question 1.

Find Taylor series for 𝑓(π‘₯) = ln(π‘₯) at x=1.
Use MATLAB to plot 𝑓(π‘₯) = ln(π‘₯) for π‘₯ ∈ (0, 5], along with Taylor approximations around π‘₯ = 1 with 𝑛 = 0, 2, 4, 6.

Question 2.

Find Taylor series for 𝑓(π‘₯) = sin(2π‘₯) at π‘₯ = πœ‹

Use an appropriate Taylor series to write a MATLAB function Mfile that approximates 𝑓(π‘₯) = sin(2π‘₯) for all x with a maximum error of 0.01. That is, your Mfile should take values of x as input, and return values of sin(2π‘₯) as output, but should not use MATLAB’s builtin sine function i.e., sin.m. Hint. You might find MATLAB’s builtin function mod useful in dealing with the periodicity.

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