I need help

you must show sufficient work to get any points Problem 1. (14') Convert from polar coordinates to rectangular, for the equation - 8 cos 0 What's the shape of the equation? To receive full credit, you need to sketch the graph and mark important data. Problem 2. (17') (1) Find the MacLaurin series for f(x) = In(1 + 2x3) and determine the interval on which this expansion is valid. (2) Find the first 4 terms in the MacLaurin series for f(x) = , (up to the cubic power). Problem 3. (14') Determine the distance travelled by a bug on the following parametric curve x(t) = sin' (t), y(t) = cos3(t), from t = 0 to t = T. Problem 4. (14') Compute the area outside of the curve r = 4 + 2 sin 0 but inside the curve r = 2 - 2 sin 0. Problem 5. (17') (1) Find the equation of the tangent line to the curve defined by the equations x(t) = 1 + +2, y(t) = 2+3 - 1 at t = 2; (2) Find the surface area generated when the plane curve defined by the equations x (t) = +3, y (t ) = 12, 0