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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 12.5 : Functions of Several Variables
For problems 1 – 6 find the domain of the given function.
- \(f\left( {x,y} \right) = \sqrt {2x + 4y - 1} \)
- \(\displaystyle f\left( {x,y} \right) = \ln \left( {\frac{1}{{x - y}}} \right)\)
- \(\displaystyle f\left( {x,y} \right) = \sqrt {\frac{1}{{{x^2}}} - \frac{1}{{{y^2}}}} \)
- \(\displaystyle f\left( {x,y,z} \right) = \frac{1}{{x + 1}} + \frac{1}{{y - 1}} + \frac{1}{{x + y - z}}\)
- \(f\left( {x,y,z} \right) = \ln \left( {{x^2} + {y^2} - 8z} \right)\)
- \(f\left( {x,y} \right) = \sqrt {x + y} - \sqrt {x - 3} \)
For problems 7 – 11 identify and sketch the level curves (or contours) for the given function.
- \({x^2} - 4z - y = 2\)
- \(x - 4z - {y^2} = 2\)
- \({z^2} + 4{x^2} = 1 - 4{y^2}\)
- \(z + 4{x^2} = 1 - 4{y^2}\)
- \(2x - 6y + z = - 2\)
For problems 12 – 14 identify and sketch the traces for the given curves.
- \({x^2} - 4z - y = 2\)
- \({z^2} + 4{x^2} = 1 - 4{y^2}\)
- \(2x - 6y + z = - 2\)