Proving the limit of sinx/x as x approaches 0 equals 1

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  • Thread starter Terrell
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this is a geometric proof from James Stewart's calculus textbook page 192. I'm confused in the sequence of inequalities as part of the proof...
theta = arcAB < AB + EB ==> arcAB < AE + ED. How did EB turned into ED?
please check the picture I've uploaded with this post
 

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QuantumQuest
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In the first diagram, it' easy to see that ##\left|EB\right| < \left|ED\right|##, so what you ask follows. Then there are just substitutions.
 
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  • #3
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Point D was described in the first half of the proof. It should be clear that |ED| > |EB|.
The benefit of doing the substitution is that you can reduce the expression to one involving straight segments related to theta by trigonometric functions.
##\tan \theta = \frac{|AD|}{|OA|}##
 
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