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Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimalplaces).$\lim _{x \rightarrow 2} \frac{x^{2}-2 x}{x^{2}-x-x}$$x=2.5,2.1,2.05,2.01,2.005,2.001,$1.9,1.95,1.99,1.995,1.999

$\lim _{x \rightarrow 2} \frac{x^{2}-2 x}{x^{2}-x-x}=1$

Calculus 1 / AB

Chapter 2

Limits

Section 3

Limits of Functions at Finite Numbers

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we want to guess the value of the limit if it exists by evaluating our function here at all the values they ask us to now, one thing. I think there's a typo in this question. Uh, I believe the denominator should be X squared minus X minus two, because otherwise checking with the answer they give in the back of the book gives something completely different from what we would get from the original one. So that's why I went ahead and made that substitution of replacing that extra negative X with negative, too. Because otherwise we wouldn't get what they have in the back of the book, Right? So I'm gonna head in, just made a Excel spreadsheet to help What's with this? So as we approach X for two from the left, it looks like the values are getting kind of like 0.666 and then from the right, it also looks like it's going to 0.666 So we might make a guess that this is just gonna be 0.6 repeating or two thirds. So this here is what we might make to be our guests of the limit as X approaches to of that function that we have up there

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