IFY Mathematics Coursework Part1
TASK 1
Inthe early 18% century彈 人
imate value of a 抽
developed a wa全 fd an ap僻!
the form of an !硬汕ite s汪稅5 and is shown below:
athematicianz Calle ed Colin Maclaurinz
lon. Itisim
人6 二(0二刻(0x二十二(0二
表
[a] ep 二+ whereais positve and nthe for where zand
are integers and 2 1 Find 刻G0, 了Go and ///G). [Note: 9
rn as
difereglon of (e+207 is 5Gz+2g9 1and follows the same pi
the diferentiation of powers ofx]」 和Go) Cr = 廬外
下 AA
條0
0
全位 )
[b] Find nurherical values of /(0), 了(0 和and ro00). [2
[cj Choose avalue ofFx (which lies between 1 and 1) and use your
Calculator to work out the value of_(1+2z8 with your chosen values ofx
and兄 [
[d] Work out /(0) +了(0, then 7(0) 十刻(0x十二(0z2, and then
7(0) 十思(0)x十二/(0)x2二二(0)x. What do you notice? [4
[e] Now choose adifferent value ofx (which also lies between ~-1and 1)
and repeat part [d]. What else do you notice? [4]
Version1 1920,