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 ${10}^{-8}.$ For the purpose of this exercise, you can approximate

the $L_2$ error as

$E_M=\frac{}{100}{\displaystyle \underset{i=1}{\overset{100}{}}}(S(x_i)-{\displaystyle \underset{n}{\overset{M}{}}}{B}_n{T}_n(x_i){)}^2,x_i=i\frac{}{100}$

$($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 $B_n\text{'}$s$.$ For extra fun, repeat the exercise but replace $x_i=i\frac{}{100}$ with $x_i=(i-1)\frac{}{100}$ above.

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