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University of Southern California

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Problem 6

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.

$$\lim _{x \rightarrow 3} \frac{x-3}{x^{2}-9}$$

Answer

$$\lim _{x \rightarrow 3} \frac{x-3}{x^{2}-9} \approx \frac{1}{6}$$

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## Discussion

## Video Transcript

we're asked to evaluate this limit numerically, so let's go ahead and do this together. So what we're gonna do is simply plug in this excess whatever this act is equal to which in this case, extralegal the three. So we're gonna go ahead and simplify it. Simplifying it leads to the limit as X approaches three of one over X plus three. Fantastic. So if you go ahead and we played in the value of acts here just like that, we get that one over. Three plus three was three plus three. That's six turns into 1/6 and that's our answer.