Compute the discriminant D(x, y). (Express numbers in exact form. Use symbolic notation and fractions where needed.) D(x, y) =
Compute the discriminant D(x, y). (Express numbers in exact form. Use symbolic notation and fractions where needed.) D(x, y) =
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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![### Compute the Discriminant \( D(x, y) \)
Please compute the discriminant \( D(x, y) \).
**Instructions**:
- Express numbers in their exact form.
- Use symbolic notation and fractions where necessary.
\[ D(x, y) = \underline{\hspace{400px}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe132a23b-2bfe-4f64-9635-6f1845f8e4fa%2F53d32a51-b5a2-48db-8079-f65e44ed4c0f%2Ffxkfdji_processed.png&w=3840&q=75)
Transcribed Image Text:### Compute the Discriminant \( D(x, y) \)
Please compute the discriminant \( D(x, y) \).
**Instructions**:
- Express numbers in their exact form.
- Use symbolic notation and fractions where necessary.
\[ D(x, y) = \underline{\hspace{400px}} \]
![The function given is:
\[ f(x, y) = x^3 y + 12x^2 - 8y + 4 \]
This is a multivariable function where \( f(x, y) \) depends on both \( x \) and \( y \). The terms of the function include:
- \( x^3 y \): This term involves both variables \( x \) and \( y \), with \( x \) raised to the third power and multiplied by \( y \).
- \( 12x^2 \): This term involves only \( x \), raised to the second power and multiplied by 12.
- \( -8y \): This term involves only \( y \), multiplied by -8.
- \( 4 \): This is a constant term.
This type of function can be analyzed to understand how changes in \( x \) and \( y \) affect the value of \( f(x, y) \), and can be visualized in three-dimensional space to see how the surface described by this equation behaves.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe132a23b-2bfe-4f64-9635-6f1845f8e4fa%2F53d32a51-b5a2-48db-8079-f65e44ed4c0f%2Fyo6x49x_processed.png&w=3840&q=75)
Transcribed Image Text:The function given is:
\[ f(x, y) = x^3 y + 12x^2 - 8y + 4 \]
This is a multivariable function where \( f(x, y) \) depends on both \( x \) and \( y \). The terms of the function include:
- \( x^3 y \): This term involves both variables \( x \) and \( y \), with \( x \) raised to the third power and multiplied by \( y \).
- \( 12x^2 \): This term involves only \( x \), raised to the second power and multiplied by 12.
- \( -8y \): This term involves only \( y \), multiplied by -8.
- \( 4 \): This is a constant term.
This type of function can be analyzed to understand how changes in \( x \) and \( y \) affect the value of \( f(x, y) \), and can be visualized in three-dimensional space to see how the surface described by this equation behaves.
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