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Write a loop in,e.g., Matlab or Python to determine terms in a sequence.

Find the first few terms of the Maclaurin and Taylor series of given functions.

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

Minitab was used to fit both an AR(1) model and an AR(2) to a stationary series. A  table is given summarising the results obtained from Minitab. Choose the most appropriate model and make a forecast based on that model.

Minitab was used to fit an AR(1) model to a stationary time series. Given the output answer the following questions about the model and use the model to make forecasts.

Power series solution of $y''+axy'+by=0$ about $x=0$.

Find the first few terms of the Maclaurin and Taylor series of given functions.

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Calculating particular harmonic components of a Fourier series expansion.

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