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

1. Jun 1, 2016

### Terrell

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?

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2. Jun 1, 2016

### QuantumQuest

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.

3. Jun 1, 2016

### RUber

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.
$\tan \theta = \frac{|AD|}{|OA|}$