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Problem 14

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.

$$\lim _{x \rightarrow-3} \frac{x^{3}+27}{x+3}$$

Answer

$$\lim _{x \rightarrow-3} \frac{x^{3}+27}{x+3} \approx 27$$

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## Discussion

## Video Transcript

you were given the following limit as X approaches Anniversary of X Q Post 27 over X plus tree and you were asked a sweet the limit by creating a table values. So we had set off by creating your table and we can see that this limit is so we have our ex inner Rex and so we basically we're trying to plug in different values of X to estimate what the limit is and so we we can poke in. Well, now you're 2.9. Then we have a goal but close sectioning with stories and another 2.99 And then we can have negative 2.999 We know at Negra history it is undefined. So there's no value. And then uh huh then we have not seen it is 3.1 93.1 in They gave three points. All right, so we can put all these different values insurer limit or into the function X Q plus. Twice I went over X plus three. We should get 36.11 26.91 there 10 and then 26.991 And then if we put you know, three points or 01 we should get 27.9 butt plug in a 3.1 We should get 27 went 0901 We put in a 3.1. We should get place of a 0.91 So you notice that these values appears to be converging to the number 27. And because of this, you know that the limit as except approaching Magnus Re of X cubed plus 27 over X plus Serie is approximately place of it.

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