Consider the following.

$f(x,y)=7x-4y$

$($a$)$ Find $f(8,5)$ and $f(8\mathrm{.}1,5\mathrm{.}05)$ and calculate $z.$

$f(8,5)=$

$f(8\mathrm{.}1,5\mathrm{.}05)=$

$z=$

$($b$)$ Use the total differential $dz$ to approximate $z.$

$dz=$