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2. Rotate the semicircle of radius 2 given by y = √(4 − x^2) about the...

2. Rotate the semicircle of radius 2 given by y = √(4 − x^2) about the x-axis to generate a sphere of radius 2, and use this to calculate the surface area of the sphere.

3. Consider the curve given by parametric equations x = 2 sin(t), y = 2 cos(t).

a. Find dy/dx

b. Find the arclength of the curve for 0 ≤ θ ≤ 2π.

4.

a. Sketch one loop of the curve r = sin(2θ) and find the area enclosed.

b. Write down, but do not evaluate, an integral that gives the arc length of this loop

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