`lim_(x -> -oo) x/(sqrt(x^2 - x))` Find the limit.

Textbook Question

Chapter 3, 3.5 - Problem 27 - Calculus of a Single Variable (10th Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Let's divide the numerator and denominator by |x|. For negative x x/|x|=-1 and x^2/|x|^2=1. So we obtain

(-1)/sqrt(1-x/|x|^2).

Now we can let x tend to minus infinity, x/|x|->0 and the entire limit is (-1)/sqrt(1-0)=-1. This is the answer.

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