Let $z=2x^2+5y^2,$ and suppose that $(x,y)$ changes from $(2,-1)$ to $(2\mathrm{.}01,-0\mathrm{.}98).$

$($a$)$ Compute $z.$

$z=$

$$

$($b$)$ Compute $dz.$

$dz=$

$$

$($c$)$ Compare the values of $z$ and $dz.$

$dz$ is a good approximation of $z.$

$dz$ is not a good approximation of $z.$