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# Evaluate the limit, if it exists.$\displaystyle \lim_{x \to 5}\frac{x^2 - 5x + 6}{x - 5}$

## does not exist

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### Video Transcript

So in this problem were asked to evaluate the limit As X approaches five of this function X squared minus five. X plus six. All over x minus five. Well, we noticed first of all that in the denominator, If we evaluate X -5 at five we get zero and you can't divide I zero. So x equals five is a vertical. Ask them to. Therefore this limit does not exist and we can see this if we graph it for a minute, if we go to a graphing calculator and enter the formula in and graph it, you see this right And x equals five. You notice that it's a vertical assam vote? There is no value of this function on on this equation. X equals five. Right? Excellent. five. There is no value of the function of the red function on that vertical aspect to it right there. So it was. So the limit, you notice that limit from the left goes to negative infinity and live from the right goes to positive infinity. As we approach from the left or the right, depending on which one you're looking at and those are not the same number. And so therefore this limit does not exist

DM
Oklahoma State University

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