Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3. Draw at least six (6) level curves for each of the following functions, choosing a reasonable contour interval. (a) f(x, y) = 4x² - y (b) f(x, y) = 7² (c) f(x, y) = x + 2y - 1 (d) f(x,y) = 2/1/2

3. Draw at least six (6) level curves for each of the following functions, choosing a reasonable contour interval. (a) f(x, y) = 4x² - y (b) f(x, y) = 7² (c) f(x, y) = x + 2y - 1 (d) f(x,y) = 2/1/2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

I am having a difficult time trying to do these parts because I don't understand the problem can you please do this step by step so I can see how you did it and can you label it as well

### Problem 3: Drawing Level Curves #### Objective: Draw at least six (6) level curves for each of the following functions, choosing a reasonable contour interval. #### Functions: **(a)** \( f(x, y) = 4 - x^2 - y \) **(b)** \( f(x, y) = x^2 \) **(c)** \( f(x, y) = x + 2y - 1 \) **(d)** \( f(x, y) = \frac{y}{x^2} \) --- #### Step-by-Step Guide: ##### 1. Understanding Level Curves: Level curves, also known as contour lines, represent the set of points where a function of two variables \( f(x, y) \) has a constant value. For a given constant \( c \), the level curve for the function \( f(x, y) \) is given by the curve formed by \( f(x, y) = c \). ##### 2. Choosing Contour Intervals: A reasonable contour interval should be chosen based on the range and nature of the function to appropriately represent the variations in the function across the domain. Here, we summarize the approach to drawing the level curves for each given function. --- #### (a) \( f(x, y) = 4 - x^2 - y \) - Identify easy values of \( c \) for contour intervals. For example, choose \( c = 0, 1, 2, 3, 4, 5 \). - Solve for \( y \) in terms of \( x \) and \( c \): \( y = 4 - x^2 - c \). - Plot these curves over a suitable domain of \( x \). #### (b) \( f(x, y) = x^2 \) - Notice \( f(x, y) \) only depends on \( x \), hence level curves are vertical lines. - Example contour values \( c = 0, 1, 2, 3, 4, 5 \). - For each \( c \), draw vertical lines at \( x = \pm \sqrt{c} \). #### (c) \( f(x, y) = x + 2y - 1 \) - Level curves are straight lines. - Choose contour values \( c = -3, -2, -1,
Transcribed Image Text:### Problem 3: Drawing Level Curves #### Objective: Draw at least six (6) level curves for each of the following functions, choosing a reasonable contour interval. #### Functions: **(a)** \( f(x, y) = 4 - x^2 - y \) **(b)** \( f(x, y) = x^2 \) **(c)** \( f(x, y) = x + 2y - 1 \) **(d)** \( f(x, y) = \frac{y}{x^2} \) --- #### Step-by-Step Guide: ##### 1. Understanding Level Curves: Level curves, also known as contour lines, represent the set of points where a function of two variables \( f(x, y) \) has a constant value. For a given constant \( c \), the level curve for the function \( f(x, y) \) is given by the curve formed by \( f(x, y) = c \). ##### 2. Choosing Contour Intervals: A reasonable contour interval should be chosen based on the range and nature of the function to appropriately represent the variations in the function across the domain. Here, we summarize the approach to drawing the level curves for each given function. --- #### (a) \( f(x, y) = 4 - x^2 - y \) - Identify easy values of \( c \) for contour intervals. For example, choose \( c = 0, 1, 2, 3, 4, 5 \). - Solve for \( y \) in terms of \( x \) and \( c \): \( y = 4 - x^2 - c \). - Plot these curves over a suitable domain of \( x \). #### (b) \( f(x, y) = x^2 \) - Notice \( f(x, y) \) only depends on \( x \), hence level curves are vertical lines. - Example contour values \( c = 0, 1, 2, 3, 4, 5 \). - For each \( c \), draw vertical lines at \( x = \pm \sqrt{c} \). #### (c) \( f(x, y) = x + 2y - 1 \) - Level curves are straight lines. - Choose contour values \( c = -3, -2, -1,
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS