Week 10 of m171
(§ 3, Mr. Lane)
3–7 April 2017

Math Learning Center (in Math 011) has tutors:
9am–4pm on Monday–Thursday and 9am–1pm on Friday

math@Mansfield (Library) has tutors: 6:30pm – 9:00pm on Sunday–Thursday

math@Mansfield (Library) has tutors: 6:30pm – 9:00pm on Sunday–Thursday

- Monday [d32] (3 Apr 2017)
WeBWorK:
RQ-4-6 closes at noon
- Section 4.6 discusses situations where several quantities are related
and each quantity can be viewed (implicitly) as a function of time.
Implicit differentiation (with respect to time) is a tool to
analyze how their rates-of-change are related.
A sequence of sketches may help you think about the dynamic ways
those quantities are related during changes as time progresses.
For instance, examine some interactive examples at (item 23 of)
- Lamp Post: shadow changes as a person moves away from a light
- Two Trains:
distance between a train going West and a train going North (drag
slider for t
**slowly**before starting animation) - Conical Tank: height of water as a cone is filled
- Falling Ladder: top of ladder slides on a vertical as its bottom is moved horizontally

- Study Examples 5 (use link, above, to
**Falling Ladder**) & 6 of §4.6 (pages 235–236). - Work on these items at end of §4.6:
**12**, 13, 15; 25,*29*, 33;**59**

- Section 4.6 discusses situations where several quantities are related
and each quantity can be viewed (implicitly) as a function of time.
Implicit differentiation (with respect to time) is a tool to
analyze how their rates-of-change are related.
A sequence of sketches may help you think about the dynamic ways
those quantities are related during changes as time progresses.
For instance, examine some interactive examples at (item 23 of)
- Tuesday [d33]
WeBWorK:
RQ-4-7 closes at noon,
day-30 closes at 11 pm
- Study section 4.7
(
*l'Hopital's Rule, Growth, and Dominance*). through Example 2 (ends at top of page 244).- Study figures 4.96 and 4.97 to develop geometric intuition for the statements of l'Hopital's Rule on page 243.
- Be careful about the logic involved here:
*discovering a ratio of derivatives does not have a limit is*.**inconclusive**about the original ratio

- Work on these items at end of §4.7:
1, 3, 5;
**16**, 17, 23, 31, 45; 67 - Resume study of §4.7 on page 244:
**l'Hopital's Rule in cases involving infinity**. - Work on these items at end of §4.7: 7, 8, 11, 14, 15; 19, 27, 29, 33, 37, 53; 64, 68
- Anticipate a quiz on Tuesday or Wednesday.

- Study section 4.7
(
- Wednesday [d34]
WeBWorK:
RQ-4-8 closes at noon,
day-31 closes Thursday at 11 pm
- Study section 4.8 (
*Parametric Equations*) through Example 9 (ends at top of page 254).- Calculus ideas in this section appear first on page 251.
- Bring a graphing tool (calculator, tablet, paper-&-pencil, etc.) to class on Wednesday.

- Work on these items at end of §4.8:
**3**, 5,**9**, 21,**27**, 33; 37, 41,**49**; 62, 64

- Study section 4.8 (
- Friday [d35]
WeBWorK:
day-32 closes Saturday at 11 pm
- Write-up solutions of these three problems —
show your work and interpret your results. Hand-in your written
homework at the
**start**of Friday's class.**section**4.4 4.6 4.7 **problems**30 38 58 - Resume study of §4.8 on page 254:
**Parametric Representation of Curves in the Plane**. - Work on these items at end of §4.8: 7, 14 & 31, 29; 39, 45, 47, 51, 53; 66, 67

- Write-up solutions of these three problems —
show your work and interpret your results. Hand-in your written
homework at the

© Richard B Lane
Last modified: 31 March 2017, Friday 07:29