University of California, Berkeley

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Problem 15

Estimating a Limit Numerically In Exereises $11-18$ ,create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result.

$$\lim _{x \rightarrow-6} \frac{\sqrt{10-x}-4}{x+6}$$

Answer

$$\lim _{x \rightarrow-6} \frac{\sqrt{10-x}-4}{x+6} \approx-\frac{1}{8}$$

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## Discussion

## Video Transcript

his. They were asked to create a table. You find the limit of this functions so it starts with X is equal to neighbor 6.1. If you plug X into our function here, our function after effects is approximately negative. 0.1248 If X is equal to negative 6.1 our function is the box. It came like that 0.12498 of X is equal to 6.1 and they're gonna love it. Our function is approximately *** of 1.124998 of X is equal to with big rallies from my right hand side. So negative 5.999 Our function is approximately they 0.1251 If X is equal to negative 5.99 Our function is approximately made of one point are not named at one point point 12501 And when X is equal to negative 5.9, our function is approximately Thank you. Point or negative point 12 five for one night. So based on this sense, on the left hand side, we're approaching made a 0.12499 week around that report, native 0.15 and then on our right hand side, we're also looking negative point. Want to fight? We can conclude that our function or the limit as X approaches they get six of our functions is approximately negative, quite 1 to 5, and this is actually equal to negative one over.

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