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sinx over x - To show lim sin 0 = 1 The following figure...

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To show: θ θ θ sin lim 0 = 1. The following figure shows a sector OAC with angle θ of a unit circle and 2 right-angled triangles OBC and OAD . Observe that (1) area of sector OAC = ½ r 2 θ = θ /2, (2) area of OBC = ½ OB · BC = ½ cos θ · sin θ , (3) area of OAD = ½ OA · AD = ½ · 1 · tan θ = ½ tan θ . By comparing the above three areas, we have:
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