### Estimating a Limit Numerically In Exereises $11-1… 00:23 University of California, Berkeley Problem 11 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 1} \frac{x-2}{x^{2}+x-6}\$

$$\lim _{x \rightarrow 1}\left[\frac{x-2}{x^{2}+x-6}\right] \approx 0.25$$

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## Video Transcript

Okay, so we're asked to create a listen, let's of values or a crisp table of the show. What the result of our women has experts is one of the functions. And so let's start with the 2.9. So we get 0.9 months to over, or a point guard plus 0.0.9 point six, which is approximately 0.25641 Now an X is equal to 0.99 our function plugging it in 0.99 for X we get. This is approximately 8.256 and then one actually good 10.999 Our function approaches 0.256 Okay, No, it's a pro approach from the right hand side. The next is equal to 1.1 our function approach it point 2439 when X is equal to one quick one function is approximately 0.2494 And when X is equal to 1.1 our function is approximate same 0.2499 So, based on what we're approaching from our lifetime side and our right hand side, we can say that our function is approaching approximately 0.25 This is approximately points