1. [11'] points) Consider the two points [1, 3) and [91A]. Find the equation of the line y ma: through the origin that "best ts11 these two points. By best ts, it means the sum of the 1.rertical distances between these points and the line is minimized. In the picture below, you are trying to nd the slope in such that the sum of the lengths of the dotted lines are minimized. [Hint: It is actually easier1 and equivalent, to minimize the square of the sums of the vertical distances] Note: This problem is a simplied 1.rersion of what is called the line of best t for a set of data points. The actual line of best t of a set of points does not have to go through the origin [like in our example}. This requirement was implemented to make the problem simpler for otherwise we would have to nd the slope and the yintereept. 2. {11'} points) Consider the top half of the circle 1'2 + y2 = l. A rectangle is formed inside the circle as show in the picture below. 1|What is the maximum area of such a rectangle? A' 1 1G 3. {Ill points) Consider the function y 2 NE. [a) Write the equation of the tangent line to this curve at :I.' = )1. (h) Draw the curve and the tangent line on the same set of axes. [c] Use the tangent line equation to estimate m [cl] Now use your calculator and write the exact value of M to 5 decimal places. {e} Perform a Google search and write down what algorithm your calculator employs to calculate square roots