f(x, y) = [x² + y² if x² + y² < 1 -2 1 if x² + y² 21
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 limit of the function on the circle
and which method is best to identify the limit
![The 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 piecewise function describes a scenario where the value of the function depends on the sum of the squares of \( x \) and \( y \):
- The expression \( x^2 + y^2 \) is used when the condition \( x^2 + y^2 < 1 \) is satisfied. This condition represents all the points inside the unit circle.
- The function is equal to 1 when \( x^2 + y^2 \geq 1 \), covering the boundary and the exterior of the unit circle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6329110f-118f-40d9-8fa0-922c549f1104%2F3021238b-71ab-4293-bfef-48dfccb2eda7%2F5x6m2rc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The 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 piecewise function describes a scenario where the value of the function depends on the sum of the squares of \( x \) and \( y \):
- The expression \( x^2 + y^2 \) is used when the condition \( x^2 + y^2 < 1 \) is satisfied. This condition represents all the points inside the unit circle.
- The function is equal to 1 when \( x^2 + y^2 \geq 1 \), covering the boundary and the exterior of the unit circle.
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