How to Transform Limit Expressions That Preclude Using L'Hôpital's Rule - dummies

# How to Transform Limit Expressions That Preclude Using L’Hôpital’s Rule

Although L’Hôpital’s rule is a great shortcut for doing limit problems, you may sometimes be unable to proceed with a limit problem when substitution produces certain unacceptable forms.

For example, when substitution of the arrow-number into the limit expression produces one of the forms

you use the following logarithm trick to turn it into an acceptable form. Here’s how it works. Say you want to find

Substitution gives you

which equals 00, so you do the following:

1. Set the limit equal to y.

2. Take the log of both sides.

3. This limit is a

case, so tweak it.

4. Now you’ve got a

case, so you can use L’Hôpital’s rule.

The derivative of

and the derivative of

5. This is a

case, so use L’Hôpital’s rule again.