QUESTION $1.$ Submit all steps, code, script, solutions, plots, etc. $[$Mark: $3]$

Use a Taylor series expansion to determine the zeroth, first, second, third and fourth order

approximations of $y(x_o+2x)$ where $x_o=O$ and $x=1.$ Plot and compare the approximations with the

exact solution by comparing percentage errors. Generate answers correct to four decimal places. The

function is

$y(x)={}_1{x}^3-{}_2{x}^2+{}_3$

Here, ${}_1,{}_2,{}_3$ are the smallest, second smallest, and third smallest non$-$zero digits, respectively, of

your student ID$.$ E$.$g$.,$ ID $=110985247$ gives ${}_1=1,{}_2=2,$ and ${}_3=4,$ i$.$e$.,f(x)=1x^3-2x^2+4.$