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Homework Statement
f(x,y,z) = 4x^2 + y^2 + 9z^2
another one is xy+z^2
how do u draw level curves and graphs for these?
Homework Equations
The Attempt at a Solution
Just need somewhere to start
Thanks
The problem with "drawing graphs" for these is that you need three orthogonal axes for the independent variables, x, y, and z, and an axes perpendicular to all of those for the function value, f. That is, you will need a four dimensional graph.1LastTry said:Homework Statement
f(x,y,z) = 4x^2 + y^2 + 9z^2
another one is xy+z^2
Level curves will help you reduce a dimension by treating the function value as a constant. That is, the level curves (more correctly "level surfaces") for for f(x,y,z)= 4x^2+ y^2+ 9z^2 will be the three dimensionl graphs 4x^2+ y^2+ 9z^2= C for different values of C. Those will be a number of ellipsoids, of different sizes, one inside the other.how do u draw level curves and graphs for these?
Homework Equations
The Attempt at a Solution
Just need somewhere to start
Thanks
The type of graph you choose depends on the type of data you want to represent. If you want to show a relationship between two variables, a scatter plot is a good choice. If you want to represent categorical data, a bar graph or pie chart would be more appropriate. If you want to compare values over time, a line graph is often used.
The x-axis represents the independent variable and the y-axis represents the dependent variable. Make sure to label each axis with the appropriate variable and include units if applicable. The title of your graph should be succinct and accurately describe what the graph is showing.
Level curves, also known as contour lines, are lines on a graph that connect points with the same value. They are commonly used to represent three-dimensional surfaces on a two-dimensional graph. To draw them, you will need to plot several points on the graph and connect them with a smooth curve.
The scale of your graph refers to the interval between each tick mark on the axes. It is important to choose a scale that clearly shows the data without distorting the graph. One way to do this is to start with a small interval and adjust as needed to fit the data.
Some common mistakes to avoid include mislabeling axes, using the wrong type of graph for the data, not including a title, and distorting the scale to make the data appear more significant. It is also important to make sure your graph is neat and easy to read.