Linear approximation question of ##xy−5y^2##

[A330NEO]

First, I already know that when we have to do linear approximation of $f(x, y)$ if $\Delta z = f_{x}(a, b)\Delta x + f_{y}(a, b)\Delta y + \epsilon_{1}\Delta x + \epsilon_{2}\Delta y$. and $\epsilon_{1}$ and $\epsilon_{2}$ approaches to nought wneh $(\Delta x, \Delta y)$ approaches zero. But how can I find appropriate value of $\epsilon_{1}$ and $\epsilon_{2}$? in this question for example, epsilons of $z = f(x, y) = xy-5y^2$?

 

[Mark44]

First, I already know that when we have to do linear approximation of $f(x, y)$ if $\Delta z = f_{x}(a, b)\Delta x + f_{y}(a, b)\Delta y + \epsilon_{1}\Delta x + \epsilon_{2}\Delta y$. and $\epsilon_{1}$ and $\epsilon_{2}$ approaches to nought wneh $(\Delta x, \Delta y)$ approaches zero. But how can I find appropriate value of $\epsilon_{1}$ and $\epsilon_{2}$? in this question for example, epsilons of $z = f(x, y) = xy-5y^2$?

First off, do not delete the three parts of the template. They are there for a reason.

The formula you show for $\Delta z$ gives the exact change in z (or in your case, f). What you're after is a linear approximation, so you can ignore the two terms with $\epsilon$.