Question $2.(10$ points each$)$ For each of the functions S$($x$)$ above, calculate how many terms in the series

you need to add to have a L$2$ error less than $108.$ For the purpose of this exercise, you can approximate

the L$2$ error as

EM $=\backslash$pi

$100$

X$100$

i$=1$

S$($xi$)$

MX

n

BnTn$($xi$)$

$!2$

$,$ xi $=$ i

$\backslash$pi

$100.$

$($Hint: Unless you plan to spend a lot of quality time with your pocket calculator, this exercise is best

done with the aid of a Matlab script.$)$ For the purpose of the number of terms, report only those that have

non$-$zero Bn$$s$.$ For extra fun, repeat the exercise but replace xi $=$ i$\backslash$pi $/100$ with xi $=($i $1)\backslash$pi $/100$ above.

Does anything change?