Determine the set of points at which the function is continuous. f(x, y) = x²y³ 6x² + y² 1 •{(x y) | (x, ‚ y) ‡ (0, 0 O {(x, y)ixe R and y ER} € o{kx, y) XE Randy z 0} 0 {(x, y) 1 x + y * 0} # O 0 {(x,x) x > 0 and y>0} if (x, y) = (0, 0) if (x, y) = (0, 0)
Determine the set of points at which the function is continuous. f(x, y) = x²y³ 6x² + y² 1 •{(x y) | (x, ‚ y) ‡ (0, 0 O {(x, y)ixe R and y ER} € o{kx, y) XE Randy z 0} 0 {(x, y) 1 x + y * 0} # O 0 {(x,x) x > 0 and y>0} if (x, y) = (0, 0) if (x, y) = (0, 0)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Determine the set of points at which the function is continuous.**
\[ f(x, y) =
\begin{cases}
\frac{x^2 y^3}{6x^2 + y^2} & \text{if} \ (x, y) \ne (0, 0) \\
1 & \text{if} \ (x, y) = (0, 0)
\end{cases}
\]
**Options:**
- \( \left\{ (x, y) \mid (x, y) \ne (0, 0) \right\} \)
- \( \left\{ (x, y) \mid x \in \mathbb{R} \text{ and } y \in \mathbb{R} \right\} \)
- \( \left\{ (x, y) \mid x \in \mathbb{R} \text{ and } y \ne 0 \right\} \)
- \( \left\{ (x, y) \mid x \cdot y \ne 0 \right\} \)
- \( \left\{ (x, y) \mid x > 0 \text{ and } y > 0 \right\} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97b7422a-52f7-4bc4-acdc-28b7d7bc43e4%2F4022d889-5892-447e-b5d5-c2a163fdfba5%2Ffhpn6pq_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine the set of points at which the function is continuous.**
\[ f(x, y) =
\begin{cases}
\frac{x^2 y^3}{6x^2 + y^2} & \text{if} \ (x, y) \ne (0, 0) \\
1 & \text{if} \ (x, y) = (0, 0)
\end{cases}
\]
**Options:**
- \( \left\{ (x, y) \mid (x, y) \ne (0, 0) \right\} \)
- \( \left\{ (x, y) \mid x \in \mathbb{R} \text{ and } y \in \mathbb{R} \right\} \)
- \( \left\{ (x, y) \mid x \in \mathbb{R} \text{ and } y \ne 0 \right\} \)
- \( \left\{ (x, y) \mid x \cdot y \ne 0 \right\} \)
- \( \left\{ (x, y) \mid x > 0 \text{ and } y > 0 \right\} \)
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