1. Important: Cartesian coordinates view 2D space as a grid along \( x-, y \)-axes (perpendicular and parallel lines). Polar coordinates view 2D space using rotation from the positive \( x \)-axis and distance from the origin \((0,0)\). Copy the following information (in magenta) for reference in your notes. \( r \) : distance (in any direction) from the origin (0,0). Always non-negative. \(\theta \) : counter-clockwise orientation around \((0,0)\), starting from the positive \( x \)-axis. Always in radians, generally on the interval \([0,2\pi]\) Table of coordinate conversions: 2. Use this table to convert \( f(x, y)=2 x^{2}+2 y^{2}\) into polar coordinates for \( f(r,\theta)\).3. Use the information in part (1) to give upper and lower bounds for \( r \) and \(\theta \) on the solid disk enclosed by the unit circle, centered at the origin. 4. Consider Example 2 in Section 16.4(p.893) in your ebook. Review the solution evaluating the same integral via polar coordinates. It may help to copy down the steps to go over them thoroughly. Write a new iterated integral using the same \( f(x, y)\) over a quarter ring (i.e. extend the blue ring across the entire first quadrant). Include a diagram of your domain of integration. You do not have to evaluate your integral.