Question

Use differentials to approximate the change in f due to the indicated change in the independent variables. (Round your answer to three decimal places.) f(x, y) = 2x + 3y − x y ; (x, y) changes from (3, 1) to (2.95, 1.04).

Answer 1

Answer:

For a function f(x,y) in two variables we have

$df=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy$

We have

$f(x,y)=2x+3y-xy\\\\\therefore \frac{\partial f}{\partial x}=2-y\\\\\frac{\partial f}{\partial y}=3-x$

$df=(2-y)dx+(3-x)dy\\\\\Delta f=(2-y)\Delta x+(3-x)\Delta y$

Applying values we get

$df=(2-y)dx+(3-x)dy\\\\\Delta f=(2-1)(3-2.95)+(3-3)(1-1.04)\\\\\Delta f=0.05$