Question

Use differentials to approximate the change in z for the given change in the independent variables. zequalsx squared minus 3 xy plus y when (x comma y )changes from ​(2​,3​) to ​(2.05​,2.95​)

Answer 1

Answer:

0

Step-by-step explanation:

We are given that

$Z=x^2-3xy+y$

$x_1=2,y_1=3$

$x_2=2.05,y_2=2.95$

We have to find the approximate change in z by using differentials for the given change in the independent variables.

$dz=2xdx-3(xdy+ydx)+dy$

$dx=x_2-x_1=2.05-2=0.05$

$dy=y_2-y_1=2.95-3=-0.05$

Substitute the values

$dz=2(2)(0.05)-3(2(-0.05)+3(0.05))-0.05$

$dz=0.2-3(-0.1+0.15)-0.05$

$dz=0.2-0.15-0.05=0$