Let

Question

Let $f\left(x ight)=\frac{x^2-4}{x-2}$ .

Make a conjecture about the value of ${\displaystyle\lim_{x o2}\frac{x^2-4}{x-2}}$ .

Accepted Answer

Welcome back everyone using the given table of values for F FX equals X squared minus 25 divided by X minus five. What is the plausible value of the limit of X squared minus 25 divided by X minus five as X approaches five here, we have a table of X and F of X values. And for our answer choices, A says the limit is 10 B 25 C zero and D nine. Now, what's going on in our table here? Notice that it has X values, OK? And F FX values and for our X and F FX values in the top row for our X values notice that it's going from 4.9 to 4.99 to 4.999 and so on. So it's approaching five. Well, for our values in the third row of our table, the X values, OK? Or the second set of X values, it's 5.15 0.00 sorry 5.15 0.015 0.001 and so on. So it's approaching five from the right. So that means then that our FFX values will tell us the limit if they are both approaching the same value. Now, for F FX values, it's going from 9.9 to 9.99 to 9.999. And so on, notice that from our left hand side, it's approaching 10. If we look at it from the right hand side, it's going from 10.1 to 10.01 to 10.001 to 10.0001. So from the right hand side, we observe that it's also approaching 10 from the right. Therefore, it follows that the plausible value of the limit of F FX as X approaches five is 10 A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Let $f\left(x\right)=\frac{x^2-4}{x-2}$ . <IMAGE>
Make a conjecture about the value of ${\displaystyle\lim_{x\to2}\frac{x^2-4}{x-2}}$ .

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Let $f\left(x\right)=\frac{x^2-4}{x-2}$ . <IMAGE>
Make a conjecture about the value of ${\displaystyle\lim_{x\to2}\frac{x^2-4}{x-2}}$ .