Step 3 The total differential dz for the function z = x?y is dz = ydx + dy.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
icon
Related questions
Question
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.
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning