University of California, Berkeley

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Problem 9

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.

$$\lim _{x \rightarrow 0} \frac{\sin x}{x}$$

Answer

$$\lim _{x \rightarrow 0}\left[\frac{\sin x}{x}\right] \approx 1$$

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## Discussion

## Video Transcript

Okay, So when we have exited with a negative points, Woz, our function sign of native 0.1. Okay, You know what one gives us approximately 2.998 when x is equal to negative points There. All one sign of 0.1 Overnegative went. So what is approximately no 0.999 What X is equal? Negative points. So one sign of negative point goes over one over. Native 0.1 is approximately one at exit because our function is on the line because we're writing by when x is equal to 0.1 sign of 0.1 over point goes there once is approximately one when X is equal Point girl, one sign of 0.1 over 0.1 is approximately 0.999 And lastly, when X is equal to 0.1 sign of 0.1 over 0.1 is a possibly 0.99 So we could see that from our values as X approaches zero from the left and when X approaches No, from the right, we see that both of our values are approaching one. So we can say that our limit as expert, you know, a sign of X over X is equal to one

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