Homework $1$ for Numerical methods

Deadline: $30/6/2025($Hardcopy submission in the lecture$)$

Q$1/$ Calculate the approximate absolute relative percentage error $($e$)$ resulting from using:

i$)$ First Order Taylor Series

ii$)$ Second Order Tayler Series

iii$)$ Third Order Taylor Series

to approximate the function $y=sinhx$ at $x=2\mathrm{.}2$ using a reference point of $x=2.$ Show your calculations and then tabulate your answers in the following format:

$\backslash$table$[[\backslash$table$[[$Order of Taylor$],[$series$]],\backslash$table$[[$Approximate$],[$answer$]],$e$],[$First$,,-],[$Second$,,],[$Third$,,]]$

Note: For the approximate error of using order $n$ Taylor series, use the approximate answer from order n$-1$ Taylor series as reference.