43. Let P(n) be the perimeter of an n-gon inscribed in a unit circle (Figure 8). (a) Explain, intuitively, why P(n) approaches 27 as n → o. (b) Show that P(n) = 2n sin (). (c) Combine (a) and (b) to conclude that lim sin () = 1. sin e 1. (d) Use this to give another argument that lim %3D DOO n= 9 n= 6 n= 12 FIGURE 8

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