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Given z=x²+3xy-2y²

 
 
Reply Sat 14 Feb, 2015 02:44 am
Given z=x²+3xy-2y²

Estimate the change in z when x changes from 2 to 2,5 and y changes from 3 to 2,5

Thanks in advance for the help
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Type: Question • Score: 2 • Views: 633 • Replies: 3
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fresco
 
  1  
Reply Sat 14 Feb, 2015 09:12 am
@Doesnt Matter,
z(2,3)=4+18-18 =4
z(2.5,2.5)=6.25 +18.75-12.5 =12.5
Change in z is 8.5

(Its a long time since I did partial differentiation which may, for all I know, give a different result)
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fresco
 
  1  
Reply Sat 14 Feb, 2015 09:35 am
@Doesnt Matter,
I see from the help given elsewhere that the "estimate" is 9.5.
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Kolyo
 
  2  
Reply Mon 16 Feb, 2015 05:44 am
@Doesnt Matter,
Doesnt Matter wrote:

Given z=x²+3xy-2y²

Estimate the change in z when x changes from 2 to 2,5 and y changes from 3 to 2,5

Thanks in advance for the help


Use the linear approximateion formula Δz ≈ (∂z/∂x) Δx + (∂z/∂y) Δy, where the partials are evaluated at (x,y) = (2,3).

∂z/∂x = 2x + 3y = 13
∂z/∂y = 3x - 4y = -6
Δx = 0,5
Δy = -0,5
Δz = 6,5 + 3 = 9,5

So 9,5 is indeed right.
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