Calculus: L'Hôpital’s Rule & Improper Integrals

What does L’Hôpital’s Rule help you find?

The limit of a quotient of functions when direct substitution results in an indeterminate form.

What are the two main indeterminate forms L'Hopital's Rule directly addresses?

0/0 or ∞/∞

What should you do if the first application of L'Hopital's Rule results in another indeterminate form?

Apply L'Hopital's Rule again until you get a determinate form.

How can you rewrite the indeterminate form ∞ * 0 for L'Hopital's Rule?

Rewrite the expression as a quotient using reciprocals.

What is an improper integral?

A definite integral with an infinite limit of integration or an integrand with an infinite discontinuity within the interval of integration.

What are the two types of improper integrals?

Improper integrals with infinite limits of integration and improper integrals with infinite discontinuities in the integrand.

When does an improper integral converge?

When the limit exists and is finite.

When does an improper integral diverge?

When the limit does not exist or is infinite.

How do you evaluate an improper integral?

Rewrite it as a limit and evaluate the limit.

What is a useful technique for determining if an improper integral converges or diverges without direct evaluation?

Compare it to a known convergent or divergent integral using the Comparison Test.