We want to compute an approximation to e/6 given by Pn(1/6) where Pn(x) is the Taylor...

Transcribed Image Text:

We want to compute an approximation to e¹/6 given by Pn(1/6) where Pn(x) is the Taylor polynomial of degree n about a = 0 of the function e. Find n as small as possible to ensure that the absolute error satisfies |e¹/6 – Pn(1/6)| ≤ 10-¹4? Note: since e ≤ (6/5)6 you can use the bound e¹/6 ≤ 6/5. Remark: you are not asked to give the polynomial Pn(x). We want to compute an approximation to e¹/6 given by Pn(1/6) where Pn(x) is the Taylor polynomial of degree n about a = 0 of the function e. Find n as small as possible to ensure that the absolute error satisfies |e¹/6 – Pn(1/6)| ≤ 10-¹4? Note: since e ≤ (6/5)6 you can use the bound e¹/6 ≤ 6/5. Remark: you are not asked to give the polynomial Pn(x).