Lhopital

Front

What is L'Hôpital's Rule?

Back

A method for finding limits of indeterminate forms (0/0 or ∞/∞) by differentiating the numerator and denominator.

Front

When can L'Hôpital's Rule be applied?

Back

It can be applied when the limit results in an indeterminate form such as 0/0 or ∞/∞.

Front

What is the first step in applying L'Hôpital's Rule?

Back

Differentiate the numerator and the denominator separately.

Front

What is the limit of (sin x)/x as x approaches 0?

Back

1, using L'Hôpital's Rule.

Front

What is an indeterminate form?

Back

An expression that does not have a well-defined limit, such as 0/0 or ∞/∞.

Front

What is the derivative of e^x?

Back

e^x, which is useful in applying L'Hôpital's Rule.

Front

What is the limit of (1 - cos x)/x^2 as x approaches 0?

Back

1/2, using L'Hôpital's Rule.

Front

What is the second derivative test?

Back

A method to determine the concavity of a function at critical points.

Front

What is the limit of (ln x)/x as x approaches infinity?

Back

0, using L'Hôpital's Rule.

Front

What is the significance of the derivative in L'Hôpital's Rule?

Back

It allows us to simplify the limit by transforming it into a more manageable form.