Problem $3.(40$ Relative Points$)$ Consider the approximations of the quantity A:

$A=B_1-a_4\frac{h^4}{4}-a_6\frac{5h^6}{16}-$cdotsdotsdotsdots

$A=B_2-a_4\frac{h^4}{64}-a_6\frac{5h^6}{1024}-$cdotsdotsdotsdots

$($a$)$ Using the ideas and the algorithm shown in class please approximate A with $B_1$ and $B_2$;

$($b$)$ Using the expressions $B_1=\frac{4A_2-A_1}{3}$ and $B_2=\frac{4A_3-A_2}{3}$ approximate the quantity A with the help of $A_1,A_2,A_3$;

$($c$)$ What is the Big$-$Oh of the approximation.