Answer:
0
Step-by-step explanation:
We are given that
[tex]Z=x^2-3xy+y[/tex]
[tex]x_1=2,y_1=3[/tex]
[tex]x_2=2.05,y_2=2.95[/tex]
We have to find the approximate change in z by using differentials for the given change in the independent variables.
[tex]dz=2xdx-3(xdy+ydx)+dy[/tex]
[tex]dx=x_2-x_1=2.05-2=0.05[/tex]
[tex]dy=y_2-y_1=2.95-3=-0.05[/tex]
Substitute the values
[tex]dz=2(2)(0.05)-3(2(-0.05)+3(0.05))-0.05[/tex]
[tex]dz=0.2-3(-0.1+0.15)-0.05[/tex]
[tex]dz=0.2-0.15-0.05=0[/tex]
