Handwork problem: $($Hand calculations using calculator $)$

HW$1\_1$ The Maclaurin series expansion of arctan$($x$)$ is shown below

arctan$()=(1)$

$1+2$

$1+2$

$\backslash$infty

$=0$

$=$

$3$

$3+$

$5$

$57$

$7+$

$9$

$9$

add terms one at a time to estimate arctan$(0\mathrm{.}75).$ After each term is added, calculate the true and approximate

relative errors. Use your calculator for finding the $$true$$ value. Retain $5$ decimal places in your calculations.

Present your results in a tabular form like the one in Example $4\mathrm{.}1$ of the book. The template is given below,

partially filled. Fill in empty boxes and add rows if necessary. Continue your calculations until you achieve $2$

significant figures accurac