h = 11 + 5 cos 0.51t + 2 sin 0.51t Find the earliest time of the day (to the nearest minute) that the depth is half of its maximum value. Fully justify your answer. The region R is bounded by the curve y = x2 cos- x and the x-axis between x = 0 and x = 1. Show that the area of R is 2n2 - 16 A function f(x) satisfies f' (x) = sin x and f(It) = 0 Find an expression for f(x) in terms of x 7 A curve has parametric equations x = t +1/t, y = t-1/t 7a Find the equation of the normal to the curve at the point where t = 2 7b Find the coordinates of the point where the normal cuts the curve again. Fully justify your answer. A function is defined by f(x) = 11 - 8x - x2 with domain [0,3) 8a Sketch, on the same axes, the graphs with equations y = f(x) and y = f 8b Find f-(x). Fully justify your answer. Bc State the domain of f 1, giving your answer in set notation