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Evaluate the limit if it exists.$$\lim _{x \rightarrow-2} \frac{x^{2}-x+6}{x+2}$$

Does not exist

Calculus 1 / AB

Chapter 13

Limits: A Preview of Calculus

Section 2

Finding Limits Algebraically

Limits

Differentiation

Integrals

University of Michigan - Ann Arbor

Idaho State University

Boston College

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Okay, This question would like us to evaluate this limit. So, as always with these limit problems, we're going to start just by directly plugging in. So to do this, plug in negative, too. And we get four plus two plus six for 12 on top, and then negative two plus two, which is zero on the bottom. So we know we have some kind of infinite limit or it doesn't exist. So we need to test a point to sort of test the right and left hand limits to see if they match up. So we're gonna test the limit as X approaches to her negative to from the positive side first. And we just care about the signs here. So if we have a number satellite Lee bigger than negative, too. We're going to get a positive number on the bottom and then on the top, we're also gonna have a positive number. So if we approach from the positive side, we have positive divided by positive, which is positive. Infinity. And then we did the same exact thing for the left hand side. So again the top remains unchanged because we have a positive plus a positive positive. Positive still and then But on the negative side or sorry. On the bottom side, we do get it negative because we get, like, negative 2.1 plus two, which is negative. So this sided limit is negative Infinity. So since the right side limit does not equal the left side limit, our limit does not exist.

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