Question: The cylinder with equation x + y = 1 bounded by 0 z 1 is parameterized by r(u, v) = (cos u, sin u,

The cylinder with equation x + y = 1 bounded by 0

The cylinder with equation x + y = 1 bounded by 0 z 1 is parameterized by r(u, v) = (cos u, sin u, v), u = [0, 2], v [0, 1]. Modify this parameterization in the following ways: (a) Rotate the cylinder to be centered around the y-axis instead: the result should be the cylinder with equation x + z = 1 bounded by 0 y 1. (b) Shift the cylinder by 1 unit in the y-direction: the result should be the cylinder with equation x + (y 1) = 1 bounded by 0 z 1. - (c) Make the cylinder 4 times wider and 2 times longer.

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