Find the linear approximation for the following functions $at(0,0).$

$(a)z=f(x,y)=\frac{5x+1}{-7y-3}$

$f(0,0)=$

$f_x(0,0)=$

$f_y(0,0)=$

The linear approximation $toz=f(x,y)isz=$

Using this, approximate the value $off(x,y)=zat$ the point $(x,y)=(0\mathrm{.}1,-0\mathrm{.}07).$ Ensure your answer $is$ accurate $to3$ decimal places.

$z$~~

$(b)z=g(x,y)=\sqrt[\phantom{2}]{y+co{s}^2(x)}$

$g(0,0)=$

$g_x(0,0)=$

$g_y(0,0)=$

The linear approximation $toz=g(x,y)isz=$

Using this, approximate the value $ofg(x,y)=zat$ the point $(x,y)=(0\mathrm{.}1,-0\mathrm{.}07).$ Ensure your answer $is$ accurate $to3$ decimal places.

$z$~~

$(c)z=h(x,y)=ln(-7y+x+2)$

$h(0,0)=$

$h_x(0,0)=$

$h_y(0,0)=$

The linear approximation $toz=h(x,y)isz=$