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1. Given z=x²+3xy-2y² Estimate the change in z when x changes from 2 to 2,5 and y changes from 3 to 2,52. I am stuck with the math and can't figure it out as what I need to do further.3.
a=2
b=3
Δx= +0,5
Δy= -0,5
dz/dx = 2x+3y
=2(2)+3(3)
=13
dz/dy = 3x-4y
= 3(2)-4(3)
=-6
Δz=f(a+Δx ; b+Δy) - f(a,b)
=f [2+0,5 ; 3+(-0,5)] - f(2,-0,5)
=f(2,3)(0,5) + f(2,3)(-0,5)
=** This is where I am stuck.
=13(0.5) + (-6)(-0,5)
=9,5?
a=2
b=3
Δx= +0,5
Δy= -0,5
dz/dx = 2x+3y
=2(2)+3(3)
=13
dz/dy = 3x-4y
= 3(2)-4(3)
=-6
Δz=f(a+Δx ; b+Δy) - f(a,b)
=f [2+0,5 ; 3+(-0,5)] - f(2,-0,5)
=f(2,3)(0,5) + f(2,3)(-0,5)
=** This is where I am stuck.
=13(0.5) + (-6)(-0,5)
=9,5?