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Things due Monday

The derivatives of f(x) = arccsc x & f(x) = arccot x

Take home optimization test

Book section on optimization (make sure you give examples of a wide variety of problems)


Also, you have an in-class optimization test Monday and a memorization quiz Tuesday.

I'll be online most of the weekend.

Homework 10/25

p.344 #29-34, 37

Homework answers

15)
Primary: C = 2x^2 + 8xy
Limiting: 20 = yx^2; y = 20/x^2
Primary (one-variable): C(x) = 2x^2 + 160/x

17)
Primary: P = ab(a-b)
Limiting: a+b = 8; b = 8-a
Primary (one-var.): P(a) = a(8-a)(2a-8); P(a) = -2a^3 + 24a^2 - 64a

18)
Primary: A = (1/2) (l^2) sin (theta)
Limiting: None (l is a constant)

20)
Primary: P = 100 sqrt(x) + 150 sqrt(y)
Limiting: x + y = 40; y = 40 - x
Primary (one-var.): P(x) = 100 sqrt(x) + 150 sqrt (40-x)

22)
Primary: P = xy^2
Limiting: (x/2)^2 + (y/2)^2 = r^2; y^2 = 4r^2 - x^2 (limiting eq. is the pyth. thm.)
Primary (one-var.): P(x) = 4xr^2 - x^3

27)
Primary: A = xy
Limiting: y = (4-x)/(2+x)
Primary (one-var.): A(x) = x(4-x)/(2+x)

28)
Primary: V = hx^2
Limiting: 108 = 4x + h; h = 108 - 4x
Primary (one-var.): V(x) = (108 - 4x) x^2

33)
Primary: S(x) = (x - x1)^2 + (x - x2)^2 + ... + (x-xn)^2
Limiting: None

(The value of x that minimizes S(x) is (x1 + x2 + ... + xn)/n, i.e. the average of x1, x2, ..., xn.)

36)
Primary: C(x) = 30 sqrt(10000 + x^2) + 15 (200 - x)
Limiting: None

44)
Primary: T(x) = (1/3) sqrt (90000 + x^2) + (1/8) (200 - x)
Limiting: None

Upcoming Assignments

Tomorrow (Tues.): Optimization test

No later than Wednesday: book section on f(x), f '(x), & f ''(x)
(You must turn this in before Thursday so that I can give you feedback before the weekend. You may come and work on it after you are dismissed on Wednesday.)

Monday (10/29): book section on optimization.

The following Monday (11/5): book section on product rule, quotient rule, and chain rule (incl. derivatives of trig. functions)

Homework 10/12

Do problems #43 & 44 in the packet.

Homework 10/11

Do problems 15 & 29 in the packet.

Reminder

By popular demand, we will be having a memorization quiz on Wednesday.

I won't be online tonight until about 9:00 due to ultimate. If you need help before that (or just want to play some ultimate), I will be playing at 7:00 at the Dalton State College intramural fields (next to the tennis courts). Remember: these write-ups will count as a quiz grade.

Homework for the long weekend

Solve the problem you selected in class and write it up for display. While correctness will be the main component of the grade, a substantial portion will also come from how well your solution is presented. Make sure you present the problem well enough that someone unfamiliar with our class can understand the problem (even if they wouldn't understand the calculus you use to find the solution). They should also be able to understand how you set up the equation you are trying to minimize or maximize as that (probably) won't involve calculus. Also make sure you devote some words to explaining the steps you take to find the solution and that you explain the solution in the context of the problem (i.e. what the number you found means in terms of the original problem). Make sure you answer what the problem asks. if the problem asks for dimensions, give the dimensions; if it asks for area, give the area (and the dimensions that produce that area).

Since these will be displayed, make sure you only write on one side of the paper and make your solution visually appealing (diagrams and such). I'd also prefer that you use ink on unlined paper (without scribbles). Neatness will factor into the grade.

I will be checking the blog periodically Friday, Saturday, and Tuesday, but will not have access to the internet Sunday or Monday.

Homework 10/2

p.210 #18, 19 (a & b)