L'hopital's rule

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 evaluating limits that result in indeterminate forms such as 0/0 or ∞/∞.

Front

State the formula for L'Hôpital's Rule.

Back

If lim (x→c) f(x) = 0 and lim (x→c) g(x) = 0, then lim (x→c) (f(x)/g(x)) = lim (x→c) (f'(x)/g'(x)) if the limit on the right exists.

Front

What is an indeterminate form?

Back

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

Front

Provide an example of a limit that can be solved using L'Hôpital's Rule: lim (x→0) (sin x)/x.

Back

The limit evaluates to 1 using L'Hôpital's Rule.

Front

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

Back

Differentiate the numerator and the denominator separately.

Front

Can L'Hôpital's Rule be applied multiple times?

Back

Yes, if the result after applying the rule is still an indeterminate form, you can apply it again.

Front

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

Back

The limit is 1, which can be found using L'Hôpital's Rule.

Front

What happens if L'Hôpital's Rule does not resolve the indeterminate form?

Back

You may need to use algebraic manipulation or other limit theorems.

Front

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

Back

The limit is 0, which can be shown using L'Hôpital's Rule.