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1. Sketch the polar function r = (θ − π/4)(θ − 3π/4) on the interval 0...

1. Sketch the polar function r = (θ − π/4)(θ − 3π/4) on the interval 0 ≤ θ ≤ 2π. Then find all lines tangent to this polar function at the point (0, 0).

2. Find the area of the region enclosed by one loop of the curve r = 5 sin(4θ).

3. Use the Monotone Sequence Theorem to determine that the following sequence converges: an = 1/ 2n+3 .

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