1. Clicker Question 1 – A. converges to 3/4 – B. converges to 1/4 – C. converges to 1/12 – D. converges to 1 – E. diverges

2. Clicker Question 2 – A. converges to ln(2) – B. converges to 2 ln(2) – C. converges to 0 – D. converges to 4 – E. diverges

3. Indeterminate Forms (10/11/10) If limits end up having the form 0 / 0,  / , 0 *  or   , they are called indeterminate. This means they can actually have any number value or be +  or - . Their value can’t be determined, hence the name! Note, for example, that every derivative is of the form 0 / 0. When you have such a form, you may be able to manipulate it algebraically to find its value.

4. L’Hopital’s Rule If an indeterminate form is in the form 0 / 0 or  / , you may be able to evaluate it by L’Hopital’s Rule, which says that the limit of the ratio will be the same as the limit of the ratio of the (separate) derivatives. Example: What is lim x->  x 2 / e x ?

5. Clicker Question 3 What is lim x->1 (x – 1) / ln(x) ? – A. 0 – B. 1 – C. -1 – D. -  – E. 

6. Looking ahead Wednesday’s class is optional. No clicker questions; no attendance taken. Test #1 is Friday. You may bring one reference sheet. Thursday at 5:30 is the lecture on Color in Mathematics (Davis). 3 bonus points.