Topic 26 = Stewart 4.4 = AP Classroom 4.7

L'Hospital's Rule is going to make taking limits much easier! Note: it can only be used if your limit is in an indeterminate form, and you MUST establish that it is before using it. L'Hop has been tested in MC and FRQ questions for the last several years.

Note the indeterminate forms below. Never write that a limit is "equal to" an indeterminate form. After the equal sign, write "indeterminate in the form: [identify the type]. Show your work to one side demonstrating what each part is equal to. It sounds like a detail, but readers will not give you credit if you write limit = $LaTeX: \frac{0}{0}$ . It is considered a "linkage error."

Indeterminate Forms:

Indeterminate Quotients: $LaTeX: \frac{0}{0}$ and $LaTeX: \frac{\infty}{\infty}$

Indeterminate Products: $LaTeX: 0\cdot\infty$ or $LaTeX: 0\cdot-\infty$

Indeterminate Differences: $LaTeX: \infty\:-\:\infty$

Indeterminate Powers:

$LaTeX: \infty^0$

$LaTeX: 1^{\infty}$

Action Items:

1. Take notes in class. If absent, review the powerpoints below and/or the extra resources, take notes as necessary (use the Notes document if you prefer), and make note of any questions you may have.

2. HW #4.4.1: p. 307 #1-5 odd; 9-15 odd; 16, 19, 22. If you find yourself unable to complete the homework, spend at least half an hour watching and annotating one of the AP Classroom videos listed below.

3. Strongly Recommended: watch and annotate AP Classroom videos 4.7 (two videos).

4. Optional Assignment: WaMap 3.2.

Resources:

Topic 26: L'Hospital's Rule
Topic 26: L'Hospital's Rule Notes (optional)
AP Classroom videos 4.7
WaMap 3.2
Homework Solutions