ChapterP: Prerequisites
SectionP.4: Factoring Polynomials
Problem 84E: The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the...
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Transcribed Image Text:Find z =
f(x, y) and use the total differential to approximate the quantity.
(2.03)²(9.03) – 22(9)
Step 1
We need a function z =f(x, y) such that the quantity can be represented by f(x + Ax, y + Ay) – f(x, y) for
some x and Ax.
Let z = f(x, y) = x
2
y.
Step 2
If (2.03)2(9.03) - 22 ·9 = f(x + Ax, y + Ay) – f(x, y) then
x = 2 and dx = Ax = 0.03
A 0.03
y =
9 and dy = Ay = 0.03
0.03
Step 3
The total differential dz for the function z = x2y is
dz =
ydx +
dy.
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