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Section 12.5 : Functions of Several Variables

For problems 1 – 4 find the domain of the given function.

1. \(f\left( {x,y} \right) = \sqrt {{x^2} - 2y} \) Solution
2. \(f\left( {x,y} \right) = \ln \left( {2x - 3y + 1} \right)\) Solution
3. \(\displaystyle f\left( {x,y,z} \right) = \frac{1}{{{x^2} + {y^2} + 4z}}\) Solution
4. \(\displaystyle f\left( {x,y} \right) = \frac{1}{x} + \sqrt {y + 4} - \sqrt {x + 1} \) Solution

For problems 5 – 7 identify and sketch the level curves (or contours) for the given function.

1. \(2x - 3y + {z^2} = 1\) Solution
2. \(4z + 2{y^2} - x = 0\) Solution
3. \({y^2} = 2{x^2} + z\) Solution

For problems 8 & 9 identify and sketch the traces for the given curves.

1. \(2x - 3y + {z^2} = 1\) Solution
2. \(4z + 2{y^2} - x = 0\) Solution