1. Consider the implicit equation: 2 + yz-4 = 0 (a) Sketch the 2 cross sections...

 

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1. Consider the implicit equation: 2 + yz-4 = 0 (a) Sketch the 2 cross sections from the following planes: The zy plane, The yz plane. (b) What do the cross sections look like when we think of z as being fixed? What happens to the cross sections as z increases from z = 0 to z = 1? (c) Sketch x + y-2-4 = 0 in 3D. You can also describe in words to help communicate what you are drawing. (d) Find a parametrization for the curve at the intersection of the two surfaces given by the equations: 2 + y-2-4 = 0 and z = 2 - y. (you may need multiple equations or a in your answer) (e) convert the equation z = = 22 - y2 into cylindrical coordinates. (f) convert the equation z = z2 2 - y2 into spherical coordinates. 1. Consider the implicit equation: 2 + yz-4 = 0 (a) Sketch the 2 cross sections from the following planes: The zy plane, The yz plane. (b) What do the cross sections look like when we think of z as being fixed? What happens to the cross sections as z increases from z = 0 to z = 1? (c) Sketch x + y-2-4 = 0 in 3D. You can also describe in words to help communicate what you are drawing. (d) Find a parametrization for the curve at the intersection of the two surfaces given by the equations: 2 + y-2-4 = 0 and z = 2 - y. (you may need multiple equations or a in your answer) (e) convert the equation z = = 22 - y2 into cylindrical coordinates. (f) convert the equation z = z2 2 - y2 into spherical coordinates.