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Problem 17 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to -\infty}\frac{x - 2}{x^2 + 1} $

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Video Transcript

So here we are asked to evaluate specific limit. So we're asked to evaluate a limit as X approaches negative infinity of x minus two over x squared plus one. So with large numbers uh the constant terms are going to become in uh insignificant. So we can ignore the -2 in the plus one. So this would just be the limit as X approaches negative infinity of X divided by x square. So we can eliminate an X. So this would be one over X. For now we're just evaluating the limit as X approaches negative infinity of one over X and we can apply direct substitution here. So this would be negative one over infinity and we know that one over infinity is just to zero in this case. We could have also evaluated this by law rule where we would be taking the derivative of the numerator and the derivative denominator. So the derivative of the numerator would be one, The derivative of the Dye, Romney would be two x. So we would have to apply once again direct substitution in this case. So 1/2 times negative infinity would once again also be zero. So this gives two different ways for evaluating this limit and this is our final answer