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High School Math : Finding One-Sided Limits

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Example Question #2 : Find The Limit Of A Function

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

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

Possible Answers:

$\infty$

$-\infty$

The limit does not exist.

Correct answer:

$-\infty$

Explanation:

1overx

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

This can be illustrated by thinking of small negative numbers.

f(-.1)=-10

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.

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

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High School Math : Finding One-Sided Limits

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #2 : Find The Limit Of A Function

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