Indeterminate forms

Definition

Indeterminate forms are expressions in calculus that do not have a well-defined limit. They often appear in the context of evaluating limits and require special techniques like L'Hôpital's Rule to resolve.

5 Must Know Facts For Your Next Test

1. Common indeterminate forms include $\frac{0}{0}$, $\frac{\infty}{\infty}$, $0 \cdot \infty$, $\infty - \infty$, $0^0$, $1^\infty$, and $\infty^0$.
2. L'Hôpital's Rule is frequently used to evaluate limits that result in the indeterminate forms $\frac{0}{0}$ or $\frac{\infty}{\infty}$.
3. To apply L'Hôpital's Rule, differentiate the numerator and the denominator separately until the limit can be evaluated.
4. Indeterminate forms like $0 \cdot \infty$ or $\infty - \infty$ often require algebraic manipulation before applying L'Hôpital's Rule.
5. Not all limits that initially appear as indeterminate forms are truly indeterminate; sometimes simple algebra can resolve them without advanced techniques.

Review Questions

• What are some common examples of indeterminate forms?
• How do you apply L'Hôpital's Rule to resolve an indeterminate form?
• Why might algebraic manipulation be necessary before using L'Hôpital's Rule for some indeterminate forms?

Related terms

L’Hôpital’s Rule: A method for evaluating limits of indeterminate forms by differentiating the numerator and denominator until a determinate form is achieved.

Limit: The value that a function approaches as the input approaches some value.

$\frac{0}{0}$ Form: $\frac{0}{0}$ is an example of an indeterminate form where both the numerator and denominator approach zero. Requires special techniques like L'Hôpital's Rule to evaluate.