In Problem $3,$ consider the function F$($x$,$y$,$z$)=$z$\backslash$sqrt$($x$^(2)+$y$)+2$yz$^(-1).$

A$.$ Find the equation of the plane tangent to the surface F$($x$,$y$,$z$)=7$ at the point

$(1,3,2).$

B$.$ Starting at P$\_(0),$ suppose a small change is made to only one of the variables x$,$y$,$ or z$.$

Which variable would produce the largest change $($in absolute value$)$ in F$.$ If the

change in this variable was $0\mathrm{.}1,$ then how large would the change in F be$?$

C$.$ Using the linearization of F$,$ what distance from P$\_(0)$ in the direction of $+-($:$2,2,-1$:$)$ will

produce an approximate change in F of $0\mathrm{.}1$ units?