That's a simpler proof indeed *once* you've proved l'Hospital's rule. However, applying a 'rule' feels less illuminating.
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This is actually the sandwich or squeeze theorem proof
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θcos(θ)<sin(θ) follows from the fact that the smaller circular sector's area is less than the triangle's area: • smaller sector's area = (radius)×(arc length)/2 = cos(θ)×θcos(θ)/2, • triangle's area = (base)×(height)/2 = cos(θ)×sin(θ)/2.
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Isnt it because the arc length of the sector is less than the opp side of a right triangle?
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#GeoGebra applet: http://bit.ly/2s86X64 It seems to me clear sandwiching circular sector between two trianglespic.twitter.com/b6Wc3os9sg
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please clarify the drawing with the inner curve being labelled as θ COS(θ) is this true for non-euclidian geometry?
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straight up hieroglyphics
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Nice math. You forgot to indicate that the radius of the slice took a perfect "1" unit
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