Express f sin2 :cdrr in terms of an integral in cos2 3:. Hence evaluate g- - 2 sm xdz. 0 Let a and b be the lengths of the sides of the inscribed rectangle of the largest area within a given circle. Prove or disprove the following statement: The sides of the inscribed rectangle of the largest area have unequal length, with a = 2!). Compute the gradients of the functions f (m, y) = 3:1: + y and g(x, y) = 2:2 + y2 = 10 and nd at least two points where these gradients are scalar multiples. Determine if any of these points are extreme values of at, y) subject to the constraint of g(:1:,'y)