The astroid curve below is defined by the parametric equations x(t)=2 cos' t, y(t)= 2 sin’t. Compute the area enclosed by the astroid.

Given the polar function r = f(theta) = 4sin(2*theta) Find the average rate of change of "f" between 3pi/4 and pi, and use that rate of change to estimate the value of "r" for theta= 5pi/6

The plane r + y + z = 1 and the cylinder z? + y? = 1 intersect in a curve, as shown by the 3D model below. To find the largest value that the function f(x, y, z) = 2x + 4y + z can have on this curve, use Lagrange multipliers to maximize f subject to the constraints z + y + z = 1 and a? + y? = 1. Maximum value: