Homework Assignment for M 408D -- Shirley

Homework Assignment for M 408D -- Shirley

M 408D Spring 2024 Homework # 7

The Homework #7 solutions will be turned in at the beginning of class in a stapled, fully documented packet, folded along the center vertical line.

Part I: Section 10.1

# 10, 11, 30

Part II: Section 10.2:

# 1 (See note below), 22 (See note below), 33, 47

On #1, simplify your solution.

On #22, your final solutions must be presented using a particular required format. To view this format and the solution to a model problem:==> Click Here.

Part III: Section 10.3

# 6, 10, 20 (See note below), 35, 39

On #20, recall that sin(2z) = 2 sin(z) cos(z) .

Part IV: Section 11.11 (WITH SPECIAL INSTRUCTIONS REPLACING THOSE GIVEN IN THE BOOK)

# 14(a), 16(a), and 19(a)

Special Instructions to Replace the Instructions Given in the Textbook:

Determine the nth-Taylor Polynomial, T_n(x) centered at the given value of a .

Note: This is all you do for problem #16(a), that is, only determine the nth-Taylor Polynomial.

Then, in Problems #14(a) and #19(a) only, for the given interval c ≤ x ≤ d, do the following:

i) Evaluate T_n(c) and f(c), and compute | f(c) - T_n(c) |, which is equal to the error in using T_n(x) to approximate f(x) at the left-hand endpoint, x = c.

ii) Evaluate T_n(d) and f(d), and compute | f(d) - T_n(d) |, which is equal to the error in using T_n(x) to approximate f(x) at the right-hand endpoint, x = d.

To help you out with these, the solution for #14(a) is posted. To view this solution: ==> Click Here.

Part V: Section 10.4

# 8 (see Note below), 17, 23, 37

For #8, you might re-read Example 2 on page 487 of the textbook.

PART VI: When working these problems, refer to the handout: A Summary of the Conics Equations .

PART VI-A: Section 10.5 [Work these problems after watching the video: Conic Sections: Parabolas.]

# 4, 8, 10, 36

On #4, you do not need to sketch the graph, but sketching is OK. On #8, you do need to sketch the graph.

PART VI-B: Section 10.5 [Work these problems after watching the video: Conic Sections: Ellipses.]

# 12, 14, 18

On #14, you do not need to sketch the graph.

PART VI-C: Section 10.5 [Work these problems after watching the video: Conic Sections: Hyperbolas.]

# 20, 48

On #48, you must sketch the graph and also find an equation. It will help to read the handout: 'Drawing the Box' for Hyperbola Asymptotes .