# How to Find the Level Curves of a Function Calculus 3 | Summary and Q&A

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July 9, 2019
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The Math Sorcerer
How to Find the Level Curves of a Function Calculus 3

## TL;DR

Level curves are 2D curves obtained by setting a function equal to a constant, often resulting in familiar shapes like circles and parabolas.

## Key Insights

• 😫 Level curves are obtained by setting a function equal to a constant.
• 🎚️ Level curves can result in different shapes such as circles, parabolas, and ellipses.
• 🍁 Contour maps display the graph of all level curves of a function.
• 🎚️ Level curves in 2D are analogous to level surfaces in 3D.
• 😫 The constant used in setting the function equal to determines the specific level curve obtained.
• 🎚️ Level curves provide insights into the behavior and patterns of a function.
• 🎚️ Manipulating the equation of a level curve can reveal its specific shape, such as hyperbolas and ellipses.

## Transcript

hi everyone in this video we're going to talk about level curves so the level curves level curves these are also called contour lines so the level curves of z equals f of XY are the two dimensional curves so are the two dimensional curves two dimensional curves we get when we set Z equal to a constant so when we set Z equal to a constant so in othe... Read More

### Q: What are level curves?

Level curves are the 2D curves obtained by setting a function equal to a constant. They represent points on a function where the output remains the same.

### Q: What is the difference between level curves and level surfaces?

Level curves refer to 2D curves obtained from setting a function of two variables equal to a constant, while level surfaces refer to 3D surfaces obtained from setting a function of three variables equal to a constant.

### Q: How do you find level curves?

To find level curves, you take a function and set it equal to a constant. Then, you solve for the variables to obtain a familiar shape, such as circles, parabolas, or ellipses.

### Q: What can we learn from contour maps?

Contour maps provide a visual representation of the graph of all level curves of a function. They help in understanding the behavior and patterns of the function across different levels.

## Summary & Key Takeaways

• Level curves, also known as contour lines, are the 2D curves obtained when setting a function equal to a constant.

• The graph of all level curves is called a contour map.

• Level curves can result in shapes like circles, parabolas, and ellipses, depending on the function.