Date | November 2020 | Marks available | 4 | Reference code | 20N.2.AHL.TZ0.F_5 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Show that | Question number | F_5 | Adapted from | N/A |
Question
Assuming the Maclaurin series for and , show that the Maclaurin series for is
By differentiating the series in part (a), show that the Maclaurin series for is .
Hence determine the Maclaurin series for as far as the term in .
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
METHOD 1
attempts to substitute into
M1
A1
attempts to expand the up to and including the term M1
A1
AG
METHOD 2
attempts to substitute into M1
attempts to find the Maclaurin series for up to and including the term M1
A1
A1
AG
[4 marks]
A1A1
attempts to expand the up to and including the term M1
A1
AG
[4 marks]
METHOD 1
let
uses to form M1
A1
(A1)
attempts to equate coefficients,
M1
A1
so
METHOD 2
uses to form M1
A1
(A1)
attempts to expand the up to and including the term M1
A1
Note: Accept use of long division.
[5 marks]