Calculus III - The 3-D Coordinate System

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Section 12.1 : The 3-D Coordinate System

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5. List all of the coordinates systems (\(\mathbb{R}\), \({\mathbb{R}^2}\), \({\mathbb{R}^3}\)) that the following equation will have a graph in. Do not sketch the graph.

\[{x^3} + \sqrt {{y^2} + 1} - 6z = 2\] Show Solution

This equation has three variables and so it will have a graph in \({\mathbb{R}^3}\).

On other hand because the equation has three variables in it there will be no graph in \({\mathbb{R}^2}\)(can have at most two variables) and it will not have a graph in \(\mathbb{R}\) (can only have a single variable).