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Problem 47 Medium Difficulty

Find the limit.
$ \displaystyle \lim_{\theta \to 0} \frac {\cos \theta - 1}{2 \theta^2} $

Answer

$-\frac{1}{4}$

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Video Transcript

it's clear. So when you read here, So we have the limit. The state approaches. Zero her co sign of data on minus one over too. Wait a square. This is equal to the limit and state approaches. Zero for co sign minus one over to beta square turns co sign plus one vulgar co sign plus one which is equal to one. You make this equal to limit a state of coaches. Ciro, we're co signed. Square minus one over too. Beta square. There's one over. CO sign street of plus one. This is equal to the limit. Data approaches zero negative. Sign square over to date. A square comes one over. CO signed data close one. We continue to simplify it. Out. We get signed. Square over. Data square runs the limit as ex approach speed approaches. Zero negative one over to post time data plus two. Then this equals the limit. Estate approaches zero for sign. They, uh, over beta square time. Negative one over to co sign of zero plus two. This equals one square turns negative. One over two plus two becomes equal to negative 14