Limits as $x$ approaches one from the left

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How do I find $$\lim_{x \to 1^-} -\frac{1}{x-1}$$ Can someone please show me how to work it out algebraically?

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1 Answer

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Since $x$ is "to the left of" $1$, i.e. less than $1$, $x-1$ is negative, so $-1/(x-1)$ is positive. Since the denominator is approaching $0$ as the numerator remains fixed, what happens is what always happens in that situation. Picture the denominator being a tiny number --- say $0.0000000000001$. You're dividing the numerator by it. How many times would it go into the numerator? What kind of number do you get?

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