This problem is about approximating the function f(x, y) = e cos(3y) at some point (x, y) = (a, b) with first and second degree polynomial functions. To make the work easier, we will let (a, b) = (0,0). The first degree approximation is a tangent plane. To get started, find the first partial derivatives, and evaluate at (a, b) = (0,0). f. (0,0) = f,(0,0) = What is the Linearization of f(x, y) at (0,0)? L(x, y) = = The Linearization L(x, y) is also called the first degree Taylor Polynomial for f(x, y) centered at (a, b). The graph of f(x, y) along with the Linearization (tangent plane) at (a, b) = (0,0) is shown below. X Z y
This problem is about approximating the function f(x, y) = e cos(3y) at some point (x, y) = (a, b) with first and second degree polynomial functions. To make the work easier, we will let (a, b) = (0,0). The first degree approximation is a tangent plane. To get started, find the first partial derivatives, and evaluate at (a, b) = (0,0). f. (0,0) = f,(0,0) = What is the Linearization of f(x, y) at (0,0)? L(x, y) = = The Linearization L(x, y) is also called the first degree Taylor Polynomial for f(x, y) centered at (a, b). The graph of f(x, y) along with the Linearization (tangent plane) at (a, b) = (0,0) is shown below. X Z y
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How do you approximate the function?
Transcribed Image Text:This problem is about approximating the function f(x, y) = e cos(3y) at some point (x, y) = (a, b) with
first and second degree polynomial functions. To make the work easier, we will let (a, b) = (0,0).
The first degree approximation is a tangent plane. To get started, find the first partial derivatives, and
evaluate at (a, b) = (0,0).
f(0,0) =
f,(0,0)=
What is the Linearization of f(x, y) at (0,0)?
L(x, y) =
The Linearization L(x, y) is also called the first degree Taylor Polynomial for f(x, y) centered at (a, b). The
graph of f(x, y) along with the Linearization (tangent plane) at (a, b) = (0,0) is shown below.
X
Z
Transcribed Image Text:This problem is about approximating the function f(x, y) = e cos(3y) at some point (x, y) = (a, b) with
first and second degree polynomial functions. To make the work easier, we will let (a, b) = (0,0).
The first degree approximation is a tangent plane. To get started, find the first partial derivatives, and
evaluate at (a, b) = (0,0).
f(0,0) =
f,(0,0)=
What is the Linearization of f(x, y) at (0,0)?
L(x, y) =
The Linearization L(x, y) is also called the first degree Taylor Polynomial for f(x, y) centered at (a, b). The
graph of f(x, y) along with the Linearization (tangent plane) at (a, b) = (0,0) is shown below.
X
Z
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