Points, Vectors, and Functions Exercises

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• It looks like . Within those values of θ, the value of r can be anything nonnegative, so the appropriate bound is 0 ≤ r. It would be possible to describe this region in a way that allowed r to be negative, but there's no need to go to the extra trouble.

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• The value of r can be anything greater than 2, therefore 2 ≤ r. Since the region wraps all the way around, bounds for θ are optional. We could say 0 ≤ θ ≤ 2π or we could decline to give any bounds for θ.

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• Counting the rays and the rings, we see that and 2 ≤ r ≤ 3.

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• Since no bounds are given for r, this region will extend outward infinitely. The conditions on θ include all of the third quadrant.

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• The condition r < 4 describes the inside of a circle of radius 4, not including the boundary of the circle. Since no bounds are given for θ the region wraps all the way around the origin.

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• The conditions on θ and r describe the crust of a pizza slice lying below the positive x-axis.