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Twice
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Member warned that the homework template must be used, together with some effort.
How do I know where to put the axes for the equation 4x^2 - 9y^2 = z when graphing in 3d?
Which plane? You have a hyperbolic paraboloid there.Twice said:Thank you. Can you please explain to me how to sketch the plane on the axes?
Right, thanks, I meant how do I draw the hyperbolic paraboloid on the axes?fresh_42 said:Which plane? You have a hyperbolic paraboloid there.
View attachment 233623
https://www.wolframalpha.com/input/?i=4x^2+-+9y^2+=+z
Planes are relatively easy to sketch. One uses the intersections with the "three walls" (x=0;y=0;z=0) to get an impression of a plane.
That's indeed not an easy task. I would start step by step along different values of ##z##. Maybe you will need to change the order of the coordinates to improve the picture, but that can only be said after you saw what it looks like. The link above got you how it would look like and it's very curved. Maybe there are better graphic programs out there, but I don't know them. (Of course there are, but I meant the freely available ones.)Twice said:Right, thanks, I meant how do I draw the hyperbolic paraboloid on the axes?
Twice said:Right, thanks, I meant how do I draw the hyperbolic paraboloid on the axes?
Multivariable Calculus is a branch of mathematics that deals with the study of functions of multiple variables. It extends the concepts of single-variable calculus to functions with multiple independent variables, allowing for the analysis of more complex phenomena.
Plane sketching is a method used in Multivariable Calculus to visualize a function of two variables on a two-dimensional plane. It involves plotting points and curves to represent the behavior of the function and can help in understanding its properties and relationships.
Multivariable Calculus has a wide range of applications in various fields such as physics, engineering, economics, and even medicine. It is used to model and analyze complex systems, optimize processes, and make predictions based on multiple variables.
Some important concepts in Multivariable Calculus include partial derivatives, multiple integrals, vector calculus, and the gradient, divergence, and curl operators. These concepts are essential for understanding the behavior of functions with multiple variables and their applications.
Some tips for sketching planes in Multivariable Calculus include identifying critical points and asymptotes, using symmetry to simplify the sketch, and paying attention to the behavior of the function along the coordinate axes. It is also helpful to use technology, such as graphing calculators, to aid in the visualization process.