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High School Math : Finding One-Sided Limits

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Example Question #1 : Finding One Sided Limits

Let $f(x)=\frac{1}{x}$ $\displaystyle f(x)=\frac{1}{x}$.

Find $\lim_{x\ \to \0^{-}} \frac{1}{x}$ $\displaystyle \lim_{x\ \to \0^{-}} \frac{1}{x}$.

Possible Answers:

$\displaystyle 1$

The limit does not exist.

$\infty$ $\displaystyle \infty$

$\displaystyle 0$

$-\infty$ $\displaystyle -\infty$

Correct answer:

$-\infty$ $\displaystyle -\infty$

Explanation:

1overx

This is a graph of $\frac{1}{x}$ $\displaystyle \frac{1}{x}$. We know that $\frac{1}{0}$ $\displaystyle \frac{1}{0}$ is undefined; therefore, there is no value for f(0) $\displaystyle f(0)$. But as we take a look at the graph, we can see that as $\displaystyle x$ approaches 0 from the left, f(x) $\displaystyle f(x)$ approaches negative infinity.

This can be illustrated by thinking of small negative numbers.

$\displaystyle f(-.1)=-10$

$\displaystyle f(-.01)=-100$

NOTE: Pay attention to one-sided limit specifications, as it is easy to pick the wrong answer choice if you're not careful.

$\lim_{x \to \0^+} \frac{1}{x}$ $\displaystyle \lim_{x \to \0^+} \frac{1}{x}$ is actually infinity, not negative infinity.

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High School Math : Finding One-Sided Limits

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Example Question #1 : Finding One Sided Limits

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