[CST-2] NA2 page 10

[Suchi Patel]

> Subject: [CST-2] NA2 page 10

> Dear All,

> Sorry for being stupid and useless again, but I wanted to ask for some
> clarification of the end of section 1.4.6 in Page 10 of the numerical
> analysis 2 notes, as my scribblings from lectures offer no clues.
>
> In particular:
> - in the expansion of e^x, where are the coefficients for the chebychev
> terms from? (eg 1.266T0) are they from the page 8 where the integrals
> are shown?

Our supervisor just said that it's just an example of "a" Chebyshev
approximation...but I'm really not sure how to get it!  I've tried for
hours (and given up!!!) - anyone with a better explaination, please tell
us...

> - how is the error from truncating the Taylor series after x^6
> calculated?

Since we are looking at the interval [-1, 1] we can say that the error in
truncating the Taylor series after x^6 is the maximum value of the next
terms x^7 and x^8.  i.e. 1/factorial(7) + 1/factorial(8) ~ 0.00023.
(Note: we can ignore all the other terms from x^9 and onwards as they will
make no difference, since we are considering numbers to 5 decimal places
only.)