5. Let P(n) denote the perimeter of an n-gon inscribed in a unit circle (see the following figure). n = 3 n = 6 n = 4 n = 5 n = 8 n = 7 000 (a) (2pt) Explain, intuitively, why P(n) approaches 2 as n . (b) (4pt) Show that P(n) = 2n sin (5). (Hint: Start by thinking about how to show that P(3) = 6 sin (5).) = 1 n (c) (2pt) Combine (a) and (b) to conclude that lim n sin 0 (d) (2pt) Use this to give an argument that lim 00 0 sin = 1.