Determine the equation of the level curves f(x,y) = c and sketch the level curves for the specified values of c. f(x,y) = y ;c=0, 3, 5 ..... The equation of the level curves, in terms of c, is y = : Sketch the level curves forc = 0, 3, 5. Choose the correct graph below. O A. O B. С. O D. Ay 20 5= Ay 20 20 5= Ay 2- 0 = 0 = 3 = -20 3-20 -2- -2 2. of 37/3>3
Determine the equation of the level curves f(x,y) = c and sketch the level curves for the specified values of c. f(x,y) = y ;c=0, 3, 5 ..... The equation of the level curves, in terms of c, is y = : Sketch the level curves forc = 0, 3, 5. Choose the correct graph below. O A. O B. С. O D. Ay 20 5= Ay 20 20 5= Ay 2- 0 = 0 = 3 = -20 3-20 -2- -2 2. of 37/3>3
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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Question
![**Problem:**
Determine the equation of the level curves \( f(x, y) = c \) and sketch the level curves for the specified values of \( c \).
Given:
\[ f(x, y) = \frac{y}{3} \]
Values of \( c \): \( 0, 3, 5 \)
**Questions:**
1. The equation of the level curves, in terms of \( c \), is \( y = \_\_\_\_\_\_\_\_\_\).
2. Sketch the level curves for \( c = 0, 3, 5 \). Choose the correct graph below.
**Options:**
- **A.**
- Horizontal lines at \( y = 0 \) (green), \( y = 3 \) (blue), and \( y = 5 \) (red).
- **B.**
- Diagonal lines through the origin and points (3, 3), (6, 2), representing \( y = 3x \), \( y = 5x \).
- **C.**
- Diagonal lines that intersect with the y-axis at \( y = 0 \) (green), \( y = 3 \) (blue), and \( y = 5 \) (red).
- **D.**
- Vertical lines at \( x = 0 \) and lines at \( x = 3 \), \( x = 5 \).
**Graphs Explanation:**
- **Graph A:** Displays three horizontal lines indicating constant \( y \) values for \( c = 0, 3, 5 \).
- **Graph B:** Consists of diagonal lines, none representing a clear level curve for the given function.
- **Graph C:** Shows diagonal lines that move upwards, their intersections showing different values, more complex analysis needed.
- **Graph D:** Vertical lines at given \( x \) points, which do not fit the equation of level curves.
**Correct Answer Analysis:**
For the function \( f(x, y) = \frac{y}{3} \), setting it equal to \( c \) yields:
\[ \frac{y}{3} = c \]
\[ y = 3c \]
Thus, the level curves are horizontal lines where:
- For \( c = 0 \), \( y = 0 \)
- For \( c = 3 \), \( y =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda71f516-efb8-4c35-a511-98b13aff5a74%2F8a1f4e15-3501-48fb-9879-b6578960405f%2Ffc4u6am_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Determine the equation of the level curves \( f(x, y) = c \) and sketch the level curves for the specified values of \( c \).
Given:
\[ f(x, y) = \frac{y}{3} \]
Values of \( c \): \( 0, 3, 5 \)
**Questions:**
1. The equation of the level curves, in terms of \( c \), is \( y = \_\_\_\_\_\_\_\_\_\).
2. Sketch the level curves for \( c = 0, 3, 5 \). Choose the correct graph below.
**Options:**
- **A.**
- Horizontal lines at \( y = 0 \) (green), \( y = 3 \) (blue), and \( y = 5 \) (red).
- **B.**
- Diagonal lines through the origin and points (3, 3), (6, 2), representing \( y = 3x \), \( y = 5x \).
- **C.**
- Diagonal lines that intersect with the y-axis at \( y = 0 \) (green), \( y = 3 \) (blue), and \( y = 5 \) (red).
- **D.**
- Vertical lines at \( x = 0 \) and lines at \( x = 3 \), \( x = 5 \).
**Graphs Explanation:**
- **Graph A:** Displays three horizontal lines indicating constant \( y \) values for \( c = 0, 3, 5 \).
- **Graph B:** Consists of diagonal lines, none representing a clear level curve for the given function.
- **Graph C:** Shows diagonal lines that move upwards, their intersections showing different values, more complex analysis needed.
- **Graph D:** Vertical lines at given \( x \) points, which do not fit the equation of level curves.
**Correct Answer Analysis:**
For the function \( f(x, y) = \frac{y}{3} \), setting it equal to \( c \) yields:
\[ \frac{y}{3} = c \]
\[ y = 3c \]
Thus, the level curves are horizontal lines where:
- For \( c = 0 \), \( y = 0 \)
- For \( c = 3 \), \( y =
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