# Help me graph manually, for level sets

• seto6
In summary, the conversation discusses sketching level sets for the function z=x2+y2/2(x+y). The level curve for z=0.5 is a circle, and the same method can be used for other values of z.
seto6

## Homework Statement

Characterize and Sketch several level sets for the function::

z=x2+y2/2(x+y)

N/A

## The Attempt at a Solution

i tried to set a z, for example say for z=0.5, then i get in the form of::

x+y = x2+y2

now its the difficult part, graphing it, i know doing on the computer is easy, but i want to know how to do it by hand, any tricks or tips that will make it easier to do so, rather than point by point.

same problem with z=k

2k(x+y)=x2+y2

seto6 said:

## Homework Statement

Characterize and Sketch several level sets for the function::

z=x2+y2/2(x+y)
What you have written is ambiguous, but I think you mean
$$z = \frac{x^2 + y^2}{2(x + y)}$$

You can click the equation I wrote to see my LaTeX script.

If you write it without using LaTeX, use parentheses to separate the numerator and denominator, like so:
z = (x2 + y2)/(2(x + y))
seto6 said:

N/A

## The Attempt at a Solution

i tried to set a z, for example say for z=0.5, then i get in the form of::

x+y = x2+y2

now its the difficult part, graphing it, i know doing on the computer is easy, but i want to know how to do it by hand, any tricks or tips that will make it easier to do so, rather than point by point.
The equation above is equivalent to
x2 - x + y2 - y = 0.
Complete the square in the x and y terms to see that the level curve for z = .5 is a circle.

Be advised that your equation above is not equivalent to the one you started with, since the original function is undefined if x + y = 0.
seto6 said:
same problem with z=k

2k(x+y)=x2+y2

Same thing as above should work.

got it thank you

## 1. What is manual graphing for level sets?

Manual graphing for level sets is a method used in mathematics and science to graph equations by hand. It involves plotting points on a coordinate plane to create a visual representation of a mathematical relationship between two variables.

## 2. When is manual graphing for level sets necessary?

Manual graphing for level sets is necessary when there is no readily available technology or software to graph an equation. It is also useful for understanding the relationship between variables in a mathematical equation.

## 3. How do I manually graph for level sets?

To manually graph for level sets, you will need a coordinate plane, a pencil, and an equation. Begin by choosing values for one variable and then solving for the other variable. Plot these points on the coordinate plane and then connect them to create a graph.

## 4. What are the advantages of manually graphing for level sets?

Manual graphing for level sets allows for a better understanding of the relationship between variables in an equation. It also allows for more control and customization in the graphing process. Additionally, it can be useful in situations where technology is not available.

## 5. Are there any limitations to manual graphing for level sets?

One limitation of manual graphing for level sets is the potential for human error. It can also be time-consuming and may not be as accurate or precise as graphing with technology. Additionally, some complex equations may be difficult to graph manually.

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