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Problem 45 Hard Difficulty

Find the limit.
$ \displaystyle \lim_{\theta \to 0} \frac {\sin \theta}{\theta + \tan \theta} $

Answer

$\frac{1}{2}$

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Video Transcript

it's clear. So when you read here, so we have the limit. State approaching zero. Sign Peeta over Data plus 10 gin. This is equal to when we convert it in terms of sign and co sign Tine over. Data was sign over. Go sign. We multiply both top and bottom by one over data and this gives us the limit. Must date approaches. Zero for a sign of beta. Over. Beta over one plus. Sign the data over. Data Arms one over. Co sign data. This equals the limit. State approaches zero. Signed data over Rita. Well, over the limit. Estate approaches zero. The one plus the limit. State approaches. Ciro. A sign Data over data earns the limit. State approaches zero. Everyone over co sign. You know, we get one over one plus one. Tell us. Excuse me. Multiplied by one over one. And this gives us one, huh?