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University of Southern California

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Problem 10

Estimating a Limit Numerically In Exercises $5-10$ , complete the table and use the result to

estimate the limit. Use a graphing utility to graph the function to confirm your result.

$$\lim _{x \rightarrow 0} \frac{\cos x-1}{x}$$

Answer

Using numerical, graphical and trigonometry identities the limit appears to be zero. The graphical solution confirms this result.

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## Discussion

## Video Transcript

we're asked to estimate the limit numerically. Let's so let's go ahead and do that together. So the first thing we're gonna do is apply the Hopi data room or the hospital or whatever you want to say. Which we can say that the limit as acts approaches zero. Um, we can go ahead and say that this is actually indeed negative Sign of X all over one. So what we did is we said that coastline of X minus one is in fact, just a sign of our negative sign of X. And then we replaced the ex with one on the bottom so that we go ahead typify to the limit as X approaches zero off the negative sign of X. So we go ahead and get rid of this one of the bottom. Now we're gonna go ahead and plug in. The value of X equal is zero right here. So the sign of zero is indeed zero. So this turns into zero. Our answer is zero