Week 7 of m171
(§ 3, Mr. Lane)
6–10 March 2017
Math Learning Center (in Math 011) has tutors:
10am–4pm on Monday–Thursday and
10am–1pm on Friday
math@Mansfield (Library) has tutors:
6:30pm – 9:00pm on Sunday–Thursday
- Monday [d22] (6 March 2017)
WeBWorK:
RQ-3-7 closes at noon,
day-20 closes at 11 pm
- Study section 3.7 (Implicit Functions).
- Work on these items at end of §3.7:
1, 5, 8, 9, 11, 17, 24;
33, 35, 37, 39;
42, 43, 46
- Also work on problems 63 and 65 of §3.6.
- Tuesday [d23]
WeBWorK:
RQ-3-8 closes at noon,
day-21 closes at 11 pm
- Study section 3.8 (Hyperbolic Functions).
- cosh(x) + sinh(x) = e^{x}
and
cosh(x) − sinh(x) = e^{−x}
imply
cosh^{2} − sinh^{2} = 1
- cosh is an even function and
sinh is an odd function
- The inverse function of sinh can be computed using ln,
the natural logarithm function.
- cosh′ = sinh and
sinh′ = cosh
- Work on these items at end of §3.8:
1, 3, 9, 15;
19 & 22, 23, 33;
34, 35, 40, 41, 42, 45
- Study section 3.9
(Linear Approximation and the Derivative) through Example 2.
Graph the error function for those two examples.
- Anticipate a quiz.
- Wednesday [d24]
WeBWorK:
RQ-3-9 closes at noon,
day-22 closes Thursday at 11 pm
- Study section 3.9
(Linear Approximation and the Derivative).
- Tangent lines are helpful in approximating values of a
non-linear function.
- The linear approximation for function g(x) at x = a is
L(x) = g(a) + g′(a) · (x − a).
The text has several examples computing such a linear approximation
followed by graphing g and L in the same figure.
- The Error function for a linearization is
E(x) = g(x) − L(x).
I recommend graphing that error function
on a short interval centered at x = a.
- The boxed statement on page 171 about the Error function
is important. Example 4 explains why.
- Work on these items at end of §3.9:
1, 3, 7, 9;
15, 17, 25, 39, 41;
45, 47, 48, 50
- Friday [d25]
WeBWorK:
RQ-3-10 closes at noon,
day-23 closes Saturday at 11 pm
- Write-up solutions of these four problems —
show your work and interpret your results. Hand-in your written
homework at the start of Friday's class.
section |
3.6 |
3.7 |
3.9 |
problems |
64, 66 |
32 |
16 |
- Study section 3.10
(Theorems About Differentiable Functions).
- Figure 3.44 (page 176) shows a geometric interpretation of
the Mean Value Theorem.
- The Racetrack Principle (page 177)
is a direct application of the
Increasing Function Theorem (page 176).
- Work on these items at end of §3.10:
1–9;
11, 13, 15, 19, 21, 29;
33, 34, 38–41
- Also work on problems 35 and 38 in §3.9.
© Richard B Lane
Last modified: 3 March 2017, Friday 09:16