Let

$f(x,y)=\sqrt[\phantom{2}]{x^2+y^2}$

a$)$ Find an equation of the tangent plane to the surface $z=f(x,y)$ at $(3,4)$

b$)$ Find the linear approximation of $f(x,y)$ at $(3,4)$ and use it to approximate $f(3\mathrm{.}2,3\mathrm{.}9).$

c$)$ Write the formula for differential $dz.$ Use it to compute $dz$ as x changes from $3$ to $3\mathrm{.}2$ and y changes from $4$ to $3\mathrm{.}9.$

d$)$ Compare $dz$ computed in part c$)$ to $z=f(3\mathrm{.}2,3\mathrm{.}9)-f(3,4)$