BC Calculus 09-10

Ch 5 - The Definite Integral

2009-11-16T14:27:00.002-05:00

Here's the syllabus up to Thanksgiving (mostly).

11/16 Defining the Definite Integral and looking at integration properties
           HW 5.2 p.267-268/29-47 odd and 5.3 p.274-275/1-6
11/17 Average Value
           HW 5.3 p.275-276/26, 29-42, 46
11/18 Fundamental Theorem of Calculus
           HW 5.3 p.275/7-27 odd and 5.4 p.286/1-17 odd
11/19 Derivatives of integrals with the Chain Rule
           HW 5.4 p.286-287/19-35 odd, 37-46

11/23 More problems to practice
           CW/HW 5.4 p.287-288/47-56, 60-64
11/24 Trapezoidal Rule
           HW 5.5 p.295-297/1, 3, 5-9, 11, 12, 17 (not d), 22, 23

The first sections of Ch 5

2009-11-12T20:03:00.002-05:00

11/12 Area and Riemann Sums (5.1, 5.2)
HW p.254-257/1-5,7,8,10-13,22-26 and p.267/7-27 odd

RAM Program

2009-11-10T10:07:00.002-05:00

The RAM program may be downloaded here. Please enter it into your calculator for class on Thursday.

The rest of the post test homework is p.229-231/16-18, 50, 51

More applications for derivatives

2009-10-26T09:38:00.002-04:00

Note: The sheet of extra problems was from the book: p.185/52; p.193/36, 39, 40, 50, 51

We are starting to get into the actual applications of derivatives.

10/26 4.3 Using derivatives to graph
                  HW p.204-206/8-29 by 3's, 31-39 odd, 41-48
10/27 4.4 Optimization (derivatives to find min/max)
                  HW p.214-217/1,5,7,9,15,17,20,22,25,26,28,32,34,36
10/28 4.4 AP Problem Quiz
                  HW p.217-219/39-43, 45, 47, 49
10/29 4.5 Linear Approximations (using a different book!)
                  HW HH/1-10, 14-17 and p.229-231/11-14, 52

11/02 4.5 Using the approximation
                  HW HH/11-13 and p.230-231/31-45 odd
11/03 8.1 L'Hopital's Rule (derivatives to find limits)
                  HW p.423-425/1-47 odd, 50, 52
11/04 4.6 Quick Quiz; Related Rates (everything depends on t)
                  HW p.237-239/3, 5, 6, 9, 11-13, 15, 18-22, 24
11/05 4.6 More Related Rates (because everything depends on t)
                  HW p.240-241/27, 28, 30, 32, 34, 35, 37, 39, 40, 41

11/09 Review and extra questions
11/10 Ch. 4 Test
                   HW Enter RAM program in calculator, p.229-231/16-18, 50, 51
11/11 Veterans Day - no school

Starting Derivative Applications (Ch 4)

2009-10-21T10:21:00.002-04:00

The first two sections of Chapter 4 mesh together so the homework will be a bit back-and-forth.

10/21 p.192-193/3, 5, 9, 13, 15-20, 21a, 24a, 25-33 odd
10/22 p.184-185/27-35 odd, 36, 37-43 odd, 45-51 plus a sheet of extras

Answers to today's extra questions

2009-10-19T15:35:00.002-04:00

1. For the ellipse problem today (4x^2 + 9y^2 = 36) with the generic first quadrant point (p, q), you should find the following:

xT = 9/p
yT = 4/q
xN = 5p/9
yN = -5q/4

Given that p goes from 0 to 3 and q goes from 0 to 2, we can say the following about possible values of the tangent and normal intercepts:

xT = (3, infinity)
yT = (2, infinity)
xN = (0, 5/3)
yN = (-5/2, 0)

2. For e^(2x) = k*sqrt(x) then it happens at x = 1/4 when k = 2/sqrt(e
(if you need a hint, you have two equations (original and slopes) for the two unknowns (k and x))

More with Derivatives

2009-10-06T12:20:00.002-04:00

Here is the syllabus for the rest of the chapter.

Please note that the homework after the Chain Rule class is slightly different from that posted on the board!

10/06 3.6 Chain Rule (some more)
            HW p.147-148/33-39 odd, 57, 58, 60-65, 68, 71
10/07 3.7 Implicit Differentiation
            HW p.155-156/3, 7, 11-37 odd, 40-45
10/08 3.7 Prove power rule for rational powers HW p.156-157/46-51
            3.8 Derivatives of Inverse Trig Functions
             HW p.162-163/1-19 by 3's,20,21-33 odd,34

10/12 Columbus Day, no school
10/13 3.9 Derivatives of Exp and Log Functions
            HW p.170-171/1-41 alternating odds,42,47-50,52
10/14 Professional Development - no school
10/15 3.9 Logarithmic Differentiation   HW p.170/19,20,43-46; p.172/22
           3.6 Parametrics CW p.147-148/50-58, 66, 68, 71

10/19 Review
10/20 Test of Chapter 3 Post-Test HW read 4.1, do p.184/1-25 odd

Post test homework - intro to the Chain Rule

2009-10-05T16:21:00.002-04:00

You homework is to take a peak at the Chain Rule - the last of our derivative rules. Read section 3.6 and do p.146-147/1-27 odd. I will prove it tomorrow.

Questions from today's handout

2009-10-01T20:07:00.002-04:00

You may have already noticed but at the top of today's handout of problems it mentions that you can get worked solutions for the odd problems from www.CalcChat.com (though you may need to download Shockwave to use it).

I noticed also that problem 6 is really a Chain Rule problem (sneaky cx) so you can skip that one.

Here are my answers for the even problems:
2. y - 4 = 4(x - 2) and y - 1 = -2(x + 1)
4. a] tangent y - 4 = 4(x - 2)
    b] normal   y - 4 = =0.25(x - 2)
    c] y = 0
    d] normal = curve: y = (-1/2a)(x - a) + b = x^2 (where b = a^2)
         if you use the quadratic formula to solve for x you find the
          discriminant is positive so there are two solutions.
6. skip it
14.a] v = (-27/5)t + 27 and a = -27/5
    b] v = 27(1 - .2t) = 0 so t = 5
    c] a = 5.4 ft/sec^2 rather than 32 ft/sec^2, about 1/6^th

The first half of Chapter 3

2009-09-21T14:07:00.002-04:00

This the the syllabus up to the next test. We will probably have a test after section 3.5.

9/21 Finish up the intro HW p.102-104/16-18,20,22,23,25,26,28 plus nDeriv Worksheet
9/22 Continuity, Local Linearity, etc. HW p.111-112/4-20 by 4's, 21-23,29,30 plus Smoothness Worksheet
9/23 Rules of Differentiation HW p.120/1-19 odd, 20-23, 25
9/24 Proofs of Rules HW p.120-121/27-31 odd, 33-39

9/28 Yom Kippur (no school)
9/29 3.4 (Rates of Change)
          HW p.129-133/1-3,5,8,9,12,13,16,20,21,23-32,34,36
9/30 3.5 (Trig Differentiation)
          HW p.140-141/1-13 odd,17-21,23,27-29,31-33,35
10/1 Review of 3.1-3.5 (all questions answered)

10/5 Test of 3.1-3.5
          HW read 3.6, do p.146-147/1-27 odd

Upcoming "events"
10/01 Back to School Night
10/12 Columbus Day
10/14 Professional Development Day
11/06 Term 1 ends

Computer Lab Links

2009-09-14T22:09:00.001-04:00

The computer lab deals with rate of change using actual data recorded by Mr. Richardson when he used to ride his bike from his old apartment in Bedford.

http://lhs.lexingtonma.org/Teachers/Kelly/calcbc/bikeride/

The link is to a page of Mr. Kelly's. His page mentions that the directions were handed out in class. I am going paperless with this. You will open the directions, type your answers directly into the document, and email it to me, along with any other work required. Please use a different font or color so it is easy to find your answers.

Fixing the dates on the syllabus

2009-09-14T21:34:00.002-04:00

As was pointed out in class, I forgot that we meet on Mondays, not Fridays but this really only impacted one day of the syllabus. The test is still on the 17th! Here is the updated syllabus for this week:

9/14 2.4 Rate of Change and Tangent lines
         HW p.87-90/3-21 by 3's,37,38,41,42,43
9/15 Computer Lab 700 (Bicycle Lab)
         HW finish lab and email it to me by 9/17
9/16 2.4 and Review
         HW (suggested) p.91-93/3-12 by 3's, 15,24,30,33,39-42,45,47,48,52
9/17 Ch 2 Test
         HW read section 3.1, do p.101/1-6, 11-13

To begin... Chapter 2

2009-09-07T16:12:00.005-04:00

Chapter 1 is prerequisite material that you are expected to remember so we will start with chapter 2...

Here is the plan for the whole chapter. Things may change so check back if you are not sure.

9/02 2.1 Review Limits: what they are, notation, rules for operations
               HW Worksheet of limit problems
9/03 2.1 Review 7 ways of finding limits, especially the Sandwich Theorem
               HW p.64/63 (Sandwich Thrm proof of limit of sin(x)/x as x -> 0)
9/04 no school

9/07 Labor Day
9/08 2.1 Limit of Composed Functions, substitution
               HW finish worksheet and p.64/53-56, read section 2.2
9/09 2.2 Horizontal & Vertical Asymptotes, End Behavio
               HW p.71-73/1,3,5,11-49 odd, 52-54, 56, 58, 59
9/10 2.3 Continuity and 4 kinds of Discontinuities   Half Day C B A G
               HW p.80-81 1,5,9,11,14,15-29 odd,33-38,41,42,45-47
9/11 2.4 Rate of Change and Tangent lines
               HW p.87-90/3-21 by 3's,37,38,41,42,43

9/15 Computer Lab 700 (Bicycle Lab)
               HW finish lab and email it to me by 9/17
9/16 2.4 and Review
               HW (suggested) p.91-93/3-12 by 3's, 15, 24,
               30, 33, 39-42, 45, 47, 48, 52
9/17 Ch 2 Test

        HW read section 3.1, do p.101/1-6, 11-13

Welcome!

2009-09-01T20:58:00.002-04:00

Welcome to BC Calculus. This year we will do two semesters of college calculus by May 5th, 2010 (the date of the AP Exam). After that we will do some other fun things because the math never ends...

This class goes very quickly so there are many homework problems each night, certainly more than you want to do the night before a test. KEEP UP!!! We learn lots of cool stuff and you don't want to waste time not understanding it.