7.1: 3-16, 27,28,34,36,40,43,48,49
7.2*:4,26,35,42,60,68,85
7.3*:4,10,26,32,50,58,59,70
7.4*:12,17,23,28,30,43,49,50
7.5: 8,10,17,26,31,43,44,47,50,61,64,73
8.1: 1-28
8.1: 29,30,42,45,55,57
8.2: 5,10,15,...,45,52,61
8.3: 1-30
* Extra Problem on Wed. 2/9: Two integrals were presented
in class as examples. Compute each integral in two ways. First use integration
by parts and second use a trig. identity. (If you didn't write down the
integrals then you should talk to me.
8.4: SKIP THIS SECTION
8.5: Use this as a practice section for how to choose
and use the methods of integration that you have learned.
* Write your own summary of integration methods. Use
one page and try to condense your understanding to a short list of reliable
methods.
** Write your own summary of chapter 7 material. Use
one page and try to condense your understanding to a short list of important
and useful ideas.
8.8: 1-40 (practice with improper integrals), 55,58,60,68
page 609:9,11 (You do not need to read this section to
work on these problems.)
Taylor Polynomials:
1. Find a 5th degree Taylor Polynomial
for f(x) at x=a: (Do these by hand. Show your work.)
i. e^x, a=0
ii. sin(x),
a=0
iii. cos(x),
a=0
iv. ln(x),
a=1
v. e^x, a=-2
(No decimal approximations please)
2. Find a 10th degree Taylor Polynomial
for f(x) at x=a: (Use Maple)
i. arctan(x),
a=0
ii. ln(x),
a=2
iii. tan(x),
a=pi/4
More Taylor Polynomial Problems:
1. Estimate the square root of 3.9
using linear, quadratic, and cubic Taylor Polynomials. Provide and error
estimate for each of your approximations.
2. Compute the limit as x-->0 of (cos(x)-1)/(x^2)
using Taylor Polynomials.
3. Compute the limit as x-->1 of (ln(x)/(x-1)
using Taylor Polynomials.
4. Approximate the number e using
Taylor Polynomials centered at x=0. How high must the degree of the approximation
be in order to get an approximation error less than 10^(-6) ?
Even More Taylor Polynomial Problems: See handout
7.7: 5-66(skim), 84,86,91,92,96
Two handouts on approximate integrals of sin(x) and sin(x^2)
8.7: 2,4,6,19,25,31,34,39
8.7: 26,33,35,43
Four Problems: Find the first dozen terms for each sequence.
Describe the pattern.
1. a(n+1)=(1/2)*a(n)*(1-a(n)), a(1)=1/2
2. a(n+1)=(3/2)*a(n)*(1-a(n)), a(1)=1/2
3. a(n+1)=(5/2)*a(n)*(1-a(n)), a(1)=1/2
4. a(n+1)=(7/2)*a(n)*(1-a(n)), a(1)=1/2
12.1: skim 3-46, 47,51,52,53,54,55,56,57,58,65
12.1: 60,62,63
Four Problems (again): For each of the four recursive problems mentioned above draw a cobweb diagram and reanalyze the problem.
12.2: skim 11-34 to practice identifying and analyzing
geometric series
12.2: 28,29,33,39,44,49,52,57,65,67
12.3:6,9,11,15,19,28,30,34,35
12.4:3-32(skim),33,37,38,42,45
12.5: 2-20(skim), 21,24,29,31
12.6: 2-30(skim),31,33,35
12.7: all(skim)
12.8: 3-28(skim),29,30,33,38
12.9: 5,10,14,15,20,23,26,30,39