Week 2 of m171
(§ 3, Mr. Lane)
30 Jan – 3 Feb, 2017
Math Learning Center (in Math 011) has tutors:
10am–4pm Monday–Thursday
- Your first study of a text section should be done prior to the
first class involving the topic of that section.
- Reading Question (RQ) assignments in WeBWorK will have items
to be answered while you study the cited section
before the class when its topics are first discussed.
- Each RQ–#–# assignment
will open 2 or 3 days before its topic is scheduled and
will close one hour before class on the day for that topic.
- The day–## assignments,
with a diverse collection of problems requiring more thinking,
will be open for 4–6 days and usually close at 11 pm two days
after their latest topic was introduced in class.
- Monday (30 January 2017) [d05]
WeBWorK:
RQ-1-7 closes at noon,
topics in the day-05 assignment go thru today
- Study section 1.7 (Introduction to Continuity).
- The first Reading Question assignment in WeBWorK involves this
section. Work on its problems during your first study of this
intro to continuity. This RQ-1-7 assignment closes
before class.
- After your first reading of §1.7,
close your text and write a brief summary of its ideas;
open the text and see whether your summary is adequate.
Consider how to improve your summary:
perhaps a key idea was missing,
perhaps a detail is not needed in a summary.
- pre-class Learning Objectives:
- classify simple types of discontinuity: removable, jump
- be able to use graphical conventions involving the distinction
between a solid dot and an open circle
- given a graph or (simple) formula for a function, understand
& answer question about continuity at a point
- Learning Objectives for class or further study
- apply Intermediate Value Theorem (page 55) to be able to
know an equation must
have a solution within a particular interval
- identify a scenario where a discrete phenomenon can be
usefully modeled with a continuous function
- Work on these items at end of §1.7:
1–2, 9, 14, 15;
16, 17, 21, 31, 37;
39, 43, 45, 47
- Tuesday [d06]
WeBWorK:
RQ-1-8a closes at noon,
topics in the day-06 assignment go thru today
- Study section 1.8 (Limits) through Example 5
with extra emphasis on Examples 1 & 2
- Work on these items at end of §1.8:
1, 17, 19, 21, 25, 29;
35, 39, 51, 65;
86, 89, 95
- pre-class Learning Objectives:
- one-sided limits: from below = lefthand,
righthand = from above
- the limit = two-sided limit
(both one-sided limits exist and they have same value)
- Learning Objectives for class or further study:
- Interpret figure 1.88 (page 60) carefully; e.g.,
consider its ideas in discussion of figures 1.86 and 1.87
- limit L of function F at number C involves output being
very close to L for all inputs sufficiently close to C
- Anticipate a quiz.
- Wednesday [d07]
WeBWorK:
RQ-1-8b closes at noon,
day-05 closes at 11 pm
- Study the remainder of section 1.8 (Limits) —
resume at Example 6.
- Examples 5, 6, 7 each involve a statement
that a particular limit does not exist.
Figures on page 62 show ways in which those examples differ.
Also note the two statements about Example 6:
does not exist and diverges to infinity.
- Example 8 involves ideas that were (partially) understood
several thousand years before the limits
discussed by our text in examples 1–7.
- pre-class Learning Objectives:
- limit at infinity
- infinite limit, diverge to infinity
- continuity of F at C involves both F(C) and
limit_{x to C}F(x)
[see page 63]
- Learning Objectives for class or further study:
- apply a Squeeze inequality: analyze P by finding simpler F,G
such that F ≤ P ≤ G
and F,G have same limit
- Consider whether f(x) = sqrt(x-3) is continuous at the left end
(x = 3) of its domain.
(Note: sqrt is WeBWorK's name
for the square-root function.)
Where, if anywhere, does our text discuss this detail?
- Work on these items at end of §1.8:
6, 11, 13;
40, 45, 59, 61, 63, 67, 69;
84, 88, 90–93
- Friday (3 Feb 2017) [d08]
WeBWorK:
RQ-2-1 closes at noon,
day-06 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 |
1.7 |
1.8 |
problems |
32, 36 |
28 |
- Study section 2.1 (How Do We Measure Speed?).
- Speed at a moment t=c can be
estimated by an
average speed
for a time interval containing time c.
- Average speeds over shorter time intervals containing c
are apt to yield better estimates.
- Consider the limit of such average speeds for intervals
containing c as lengths of those intervals shrink to 0.
- pre-class Learning Objectives:
- Given explicit information about position of an object as a
function of time,
find the object's position at a specified time.
- Compute average velocity of an object
during a specified time interval.
- Explain difference(s) between average velocity
and instantaneous velocity.
- Explain how velocity and speed are related.
- Work on these items at end of §2.1:
3, 5, 11;
14, 19, 21, 28;
29, 30, 36
- Learning Objectives for class or further study
- Interpret average velocity geometrically
(in terms of the graph of an object's position function).
- Given an object's position function,
compute its instantaneous velocity at a specified time
by evaluating an appropriate limit.
- Explain what a negative velocity means.
© Richard B Lane
Last modified: 30 January 2017, Monday 07:32