Find the linearization

Upper L left parenthesis x$,$y right parenthesisL$($x$,$y$)$

of the function

f left parenthesis x$,$y right parenthesisf$($x$,$y$)$equals$=$x squared minus $8$ xy plus $7$x$28$xy$+7$

at

Upper P $0$ left parenthesis $1,3$ right parenthesisP$0(1,3).$

Then find an upper bound for the magnitude

StartAbsoluteValue Upper E EndAbsoluteValueE

of the error in the approximation

f left parenthesis x$,$y right parenthesisf$($x$,$y$)$almost equals$$Upper L left parenthesis x$,$y right parenthesisL$($x$,$y$)$

over the rectangle$$ R:

StartAbsoluteValue x minus $1$ EndAbsoluteValuex$1$less than or equals$0\mathrm{.}10\mathrm{.}1,$

StartAbsoluteValue y minus $3$ EndAbsoluteValuey$3$less than or equals$0\mathrm{.}10\mathrm{.}1.$