Math 226, Fall 2002 Home & Syllabus : Assignments and Tests :Grades

### Mathematics 226: Calculus IFall 2002 Assignments and Tests

*** This is subject to change. Check back! ***

(updated 12/6/02)

Current Assignment

Date
Assignment
TA for a Day
8/28/02 Topic 0: Functions. Find the classroom. Find class web site. Buy the book.

8/29/02 Review 1.1, 1.3.

• (1.1) What are the four ways to represent a function?
• Give an example.
• (1.3) Think about the graph of f(x)=x^2. What do the graphs of f(x+2) and f(x)+2 look like?
• If g(x)=x+2, write the two previous functions as compositions of f and g.

9/3/02 Topic 1: Special Functions.
Review 1.2, 1.5, 1.6.
• (1.2) What do the graphs of sine and cosine look like?
• What are their domains? What are their ranges?
• What is the period of these functions?
• (1.5) What does the graph of f(x)=a^x look like when (i) 0<a<1, (ii) a = 1, (iii) a>1?
• Try out the laws of exponents (p.58) for the case where a=2 and x and y are integers. Do they make sense, from what you know about multiplication?
• (1.6) Exercises 1a, 1b and 2a.
• What is the horizontal line test?
Questions on HW 0?
Steven Bitner
9/4/02 Questions on HW 0?
Juliet Lao (reschedule)
9/5/02 HW 0 due: (1.1) 2, 4, 6, 8, 16, 20, 32, 34; (1.3) 4, 36, 38, 54, 56, 62

HW Quiz 0.
Susan Lai
9/10/02 Topic 2. Velocity and Limits
(get the main ideas).
• What is the definition of average velocity?
• What is the definition of instantaneous velocity?
• Consider the symbols limx->af(x) = L. Explain what this means in English.
Questions on HW1?

Lourdes Recto
9/11/02 Questions on HW1?
Jeff Miller
9/12/02 HW 1 due: (WS2) 1-5. (1.6) 20, 21, 22
Yes, and HW Quiz 1. Expect a HW Quiz every time the HW is due.
Linh Troung (reschedule)
9/17/02 Topic 3. Velocity, Tangents and Limits

Review 2.2, Read 2.3, and Skim 2.7
.

• In (2.2) Example 3, how do you use a calculator to estimate limx->0 (sin x)/ x?
• What is lim x->0 1/x^2 ?
• Give an example of a function where the left-hand limit at a point does not equal the right-hand limit at a point.
Questions on HW2?
Paul D. Wraa
(reschedule)
9/18/02 Questions on HW2? Wendy Stovall
9/19/02 HW 2 due. (WS3) 1-3, 4a. (2.1) 5, 6, 8. Extra Credit: (WS3) 4b, 4c.

BIG QUIZ.
Don't panic. This is going to be a somewhat bigger version of the usual Homework Quiz. It will be based on all past homeworks and worksheets and should take about 30-40 minutes.

9/24/02 Topic 4. Velocity, Tangents and Rates of Change

Skim 2.6 (up to but not including Precise Definitions, p.141). Read 2.7, all of it.

• Explain (2.6) Example 3.
• What is the formula of a tangent line to the graph of the curve f(x) at the point (x, f(x))?
• Find an equation of the tangent line to the parabola y=x^2 at the point (2, 4).
Questions on HW3?
Gary Bengier
9/25/02 Questions on HW3? Rahel Yohannes
9/26/02 HW3 due. (WS4) 1e, 2(all), 3a, 3b. (2.3) 2-10 even. HW Quiz too.
Jessica Hale
10/1/02 Topic 5. Derivatives and Rates of Change

Skim 2.5 (just get the definitions and ideas of the theorems). Read 2.8.

• What's the definition of the derivative of f at a number a?
• What's the relationship between the derivative of a position function at a and the idea of instantaneous velocity?
• What's the relationship between the f'(a) and the graph of f?

Questions on HW4?
Juliet Lao
10/2/02 Questions on HW4?
Wellington Chou
10/3/02 HW4 due.(2.7) 6, 8, 14ab (see Ex.3), 16-26 even. Lainya Magana (early)
10/8/02 Topic 6. Computing Derivatives

Read 2.9, 3.1 (up to Exponential Functions), 3.2.

• What is the definition of a differentiable function?
• Give an example of a function that is continuous at a point, but not differentiable.
• Write f'(a) in Leibnitz notation.
• What is the derivative of the function f(x) g(x)? (The functions f and g are multiplied pointwise.)
Questions on HW5?
Paul McGoldrick
10/9/02 Questions on HW5?
Paul Wree
10/10/02 HW5 Due. (2.8) 5-8, 15, 16, 19-24, 29, 30. (WS6) 2, 3.
Akosua Demann
10/15/02 Topic 7: Derivatives of Special Functions and Chain Rule

Read 3.1 (Exp Function part), 3.4, 3.5. You might want to review 1.3's Composition discussion.

• At what point on the curve y=e^x is the tangent line parallel to the line y=2x?
• How do you figure out the derivative of tan x from the derivatives of sin x and cos x?
• What is the Chain Rule?
Questions on HW6?
Wai-Yee Chan
10/16/02 Q on HW6?
Wellman Cheng
10/17/02 HW6 Due. (WS9) all. (2.9) 5-13, 31-34. (3.1) 10-24 even. Do (3.1) 10-24 odd for practice, but no need to submit it. Eric Chen
10/22/02 Topic 8: The Chain Rule and Related Rates

Read 3.5 (skip the Proof) and 3.10.

• What is the derivative of sin(x2) ?
• What is the derivative of (sin x)2 ?
• Air is being pumped into a spherical balloon (whose volume at time t is V(t)=(4/3)pi*r(t) as a function of the radius at time t). Write dV/dt in terms of r and dr/dt.

Q on HW7?
Gaynelle Lewis (sub)
10/23/02 Q on HW7?
Poorvi Dhabalia (reschedule)
10/24/02 HW7 Due. (3.2) 17-26, 31, 32, 35; (3.4) 8-18, 29, 30; (WS11) 1-3.
Dorian Watson (reschedule)
10/29/02 MIDTERM. Covers all work through Topic 7. You are allowed to bring one 3" x 5" index card. Calculators are allowed, but not required. You should prepare to see questions from the homework and the worksheets.

10/31/02 Halloween. Come in costume for extra credit.

HW8 Due.
(3.5) 22-40 even. Look at odd ones for practice.
Hayley Marron
11/5/02 Topic 9: Optimization and Higher Derivatives

• What is a critical number? What is their relation to local maxima/minima?
• What is the Closed Interval Method?
• What is the relationship between the sign of the second derivative of a function and its graph?
• Explain (4.7) Ex. 1.
Q on HW9?
Tommy Fulwiler
11/6/02 Q on HW9?
Eduardo Ruelas
11/7/02 HW9 Due.  (3.10) 6-20 even.
Megha Shah and Poorvi
11/12/02 Topic 10: More Optimization and Other Derivatives

Review 4.7. Learn formulas on p.230, 3.8 through Example 6.  Skim 4.2.
• What is the derivative of arctan(x)?  [Arctangent of x is the same as the inverse of tangent, sometimes written tan-1 x.]
• What is the derivative of ln (x^2) ?
• In (4.7) Ex. 2, for the paragraph beginning "Since the domain of A ...", explain
• why we can't use the argument of Ex. 1, and
• why the critical point is an absolute max, instead of just a local max.
T.J. Ross
11/13/02
Brian Oliveira
11/14/02 HW10 Due. (4.1) 8-14, 32, 34, 40, 42, 50, 54, 56, 60, 64.
Lihn T & Amanda D
11/19/02 Topic 11:  Linear Approximations and Anti-differentiation

Read 3.11 (skim differentials) and 4.10.

• What is the linearization of (x+3)^(1/2) at a = 1?
• A particle moves in a straight line and has acceleration given by a(t)=6t+4. Its initial velocity is v(0)=-6 cm/s, its initial displacement is s(0)= 9 cm. Find its position function s(t).

Brandon Yacobellis
11/20/02
Eduardo & Andrei
11/21/02 HW11 Due. (3.6) 42-48 even. (3.8) 2-10, even. (4.7) 10, 12, 14, 16, 18, 36. (WS15) 1,2.  Extra Credit: (WS13) 3.
Mireya & Dorian
11/26/02 Topic 12: Integrals and Riemann Sums

Skim 5.1 with focus on Definitions and Distance Problem. Read 5.2.

• What is the precise definition of area under a graph, as given by Stewart?
• Can you do (5.1) Example 4 with different numbers?
• What is the relationship between the definite integral of f from a to b and area?

John Gan
11/27/02 HW Quiz Today.
HW12 Due.
(3.11) 1-8, (4.10) 2, 10, 16, 30, 32, 34, 36, 45, 46, 48.
Bryant and Lawanda
11/28/02 No class, Thanksgiving Holiday
12/3/02 Topic 13: Fundamental Theorem of Calculus

• State the two Fundamental Theorems of Calculus.
• Find the area under the sine curve from 0 to Pi/4.
• What is wrong with the calculation in (5.3) Example 8?

Kasia Kappes

12/5/02 HW Quiz. HW Due: (5.1) 1-5, 11-17 Lolita Smith and Antonio F
12/10/02 Topic 14: Fundamental Theorem of Calculus II

• What is the connection between the definite integral from a to b of f(x) with the indefinite integral of f(x)?
• What is the indefinite integral of 1/x?
Clifford Anderson-Bergman
12/11/02
Joseph Flores and Chris Cheng
12/12/02 Review Day. No HW Quiz. HW (don't turn in, but it'll be on the final): (WS19) 4. (5.2) 5,7,29,30-33. (5.3) 1, 3, 5-39, odd.

12/19/02
FINAL EXAM, 1:30pm-4:00pm. 