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University of California, Berkeley

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Problem 16

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.

$$\lim _{x \rightarrow 2} \frac{[x /(x+1)]-(2 / 3)}{x-2}$$

Answer

$$\lim _{x \rightarrow 2} \frac{[x /(x+1)-(2 / 3)]}{x-2} \approx \frac{1}{9}$$

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## Discussion

## Video Transcript

Okay, so we're gonna create a table, fine its limit knowing. So it's let X equal to 1.9. We get 1.9 over 1.9 plus one to over three over 1.9 minutes to This is approximately 0.114943 Okay, so we could do the same for 1.99 I won't show the works if we're just putting that into our function rally we get. This is approximately 0.111 were a tree. The next you could feel 1.999 you get. This is approximately 0.1111148 Now, when X is equal to we get undefined. But you're subjecting two by two and are enumerated are denominated. So we're get division by now. When X is equal to if you 0.1, we get our value. Why is approximately quite 111? Go 74 Okay, so we see there are limits as experts to our function. Coaches approximately won over nine, which is equal to 2.1111 Let me check that