Date | May 2021 | Marks available | 4 | Reference code | 21M.2.AHL.TZ2.9 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | Show that | Question number | 9 | Adapted from | N/A |
Question
Write down the first three terms of the binomial expansion of (1+t)-1 in ascending powers of t.
By using the Maclaurin series for cos x and the result from part (a), show that the Maclaurin series for sec x up to and including the term in x4 is 1+x22+5x424.
By using the Maclaurin series for arctan x and the result from part (b), find limx→0(x arctan 2xsec x-1).
Markscheme
1-t+t2 A1
Note: Accept 1, and .
[1 mark]
(M1)
or (M1)
A1
A1
so the Maclaurin series for up to and including the term in is AG
Note: Condone the absence of ‘…’
[4 marks]
M1
A1
A1
Note: Condone missing ‘lim’ and errors in higher derivatives.
Do not award M1 unless is replaced by in .
[3 marks]