f(x, y) = [x² + y² if x² + y² < 1 1 if x² + y² ≥ 1
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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What is the output value of the function on the circle
and what is the domain
![The piecewise function \( f(x, y) \) is defined as follows:
\[
f(x, y) =
\begin{cases}
x^2 + y^2 & \text{if } x^2 + y^2 < 1 \\
1 & \text{if } x^2 + y^2 \geq 1
\end{cases}
\]
This function describes a rule for \( f(x, y) \) based on the sum of the squares of \( x \) and \( y \).
- If the sum \( x^2 + y^2 \) is less than 1, then \( f(x, y) \) is equal to the sum itself, \( x^2 + y^2 \).
- If the sum \( x^2 + y^2 \) is greater than or equal to 1, then \( f(x, y) \) is equal to 1.
This type of function is often used to define different behaviors in different regions of the \(xy\)-plane, sometimes related to circular areas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6329110f-118f-40d9-8fa0-922c549f1104%2F7bf6ce3f-e980-48b2-91b8-4546cd5d70d5%2Fpm0bh7n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The piecewise function \( f(x, y) \) is defined as follows:
\[
f(x, y) =
\begin{cases}
x^2 + y^2 & \text{if } x^2 + y^2 < 1 \\
1 & \text{if } x^2 + y^2 \geq 1
\end{cases}
\]
This function describes a rule for \( f(x, y) \) based on the sum of the squares of \( x \) and \( y \).
- If the sum \( x^2 + y^2 \) is less than 1, then \( f(x, y) \) is equal to the sum itself, \( x^2 + y^2 \).
- If the sum \( x^2 + y^2 \) is greater than or equal to 1, then \( f(x, y) \) is equal to 1.
This type of function is often used to define different behaviors in different regions of the \(xy\)-plane, sometimes related to circular areas.
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