MacLaurin Series | DP IB Maths: AA HL Topic Questions 2021

1a

4 marks

Consider the general Maclaurin series formula

$f (x) = f (0) + x f^{'} (0) + \frac{x^{2}}{2!} f^{''} (0) + \dots + \frac{x^{n}}{n!} f^{(n)} (0) + \dots$

(where $f^{(n)}$ indicates the $n^{t h}$ derivative of $f$ ).

Use the formula to find the first five terms of the Maclaurin series for $e^{2 x}$ .

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1b

2 marks

Hence approximate the value of $e^{2 x}$ when $x = 1$ .

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1c

3 marks

(i)

Compare the approximation found in part (b) to the exact value of

e^{2 x}

when

x = 1 .

(ii)

Explain how the accuracy of the Maclaurin series approximation could be improved.

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1d

2 marks

Use the general Maclaurin series formula to show that the general term of the Maclaurin series for $e^{2 x}$ is

$\frac{{(2 x)}^{n}}{n!}$

How did you do?

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MacLaurin Series (DP IB Maths: AA HL)