Proving the Squeeze Theorem using the Epsilon Delta Definition for the Limit
<p>Out of the many techniques there are for solving limits, the squeeze theorem is a fairly famous theorem that has the ability to evaluate certain limits by comparing with other functions. For those who do not know the squeeze theorem, it states the following:</p>
<p>Let <em>A</em> be some domain containing the point <em>c</em>, and let <em>f</em>, <em>g</em>, and <em>h</em> be defined on this common domain (except possibly at <em>c</em>). Suppose that for every <em>x</em> in A, <em>f</em>(<em>x</em>) ≤ <em>g</em>(<em>x</em>) ≤ <em>h</em>(<em>x</em>). Then, if lim(<em>x</em> → <em>c</em>) <em>f</em>(<em>x</em>) = lim(<em>x</em> → <em>c</em>) <em>h</em>(<em>x</em>) = <em>L</em>, it follows that lim(<em>x</em> → <em>c</em>) <em>g</em>(<em>x</em>) = <em>L</em>.</p>
<p>In this post, I will be going through a simple proof of this theorem using the epsilon delta definition for limits, and will finish with a simple application of this theorem.</p>
<p><a href="https://medium.com/@2305sakake/proving-the-squeeze-theorem-using-the-epsilon-delta-definition-for-the-limit-5c06eaf13e99"><strong>Read More</strong></a></p>