Short Problem Sets --- due throughout the week
Due Tuesday, May 22nd
Due Tuesday, May 22nd
- 12.1: 20, 30, 56
- 12.2: 10, 16, 24
- 12.3: 6, 18
- 12.3: 30
- 12.4: 6, 12, 18
- 12.5: 4, 8, 24, 36
- 11.6: 34
- 12.6: 4, 10, 24
- Chapter 13, Section 1: 2, 14, 22, 23
- Chapter 13, Section 2: 6, 18
- Chapter 13, Section 2: 22, 26, 36
- Chapter 13, Section 3: 6, 16, 18 [do parts 'a' and 'c' only]
- Chapter 13, Section 4: 4, 11, 17 (see the text for computing "N")
- Chapter 14, Section 1: 31-36, 39
- Chapter 14, Section 2: 16,34,46
- Chapter 14, Section 3: 18, 66
- Chapter 14, Section 4: 3, 6, 7
- First, one problem from class with 3 parts:
- a) Find the normal vector to the tangent plane to f(x,y) at (x_0, y_0) by using our equation for L(x,y).
- b) Find the equations for both tangent lines to f(x,y) at (x_0, y_0) in the x and y directions.
- c) Show that the tangent plane contains both lines.
- Chapter 14, Section 6: 9, 22, 42
- Note for #22: As you might be able to tell from reading the examples in this section, we will have more to say about this type of problem later. However another way to think about this type of problem is that it is closely related to evaluating L(x,y,z) at the right point.
- Chapter 14, Section 7: 10, 34, 51*
- Note for #51: one solves this problem by finding the local min of f(x,y,z)=x^2+y^2+z^2 (no need to justify this, but it is worth convincing yourself it is the right thing to do).
- Chapter 14, Section 8: 2, 26
- Read 15.1-15.3
- Chapter 15, Section 1: 5, 24
- Chapter 15, Section 2: 9-12, 16-18, 30
- Chapter 15, Section 5: 21, 26, 36
- Chapter 15, Section 7: 12, 52
- Chapter 15, Section 7: 32, 34, 41
- You should also be reading Chapter 16
- Chapter 16, Section 1: 9
- Chapter 16, Section 2: 9
- Due Tuesday, May 29th: Do Core Problems (pdf) from Chapter 12, Sections 1-6 + Chapter 11, Section 6
- Due Monday, June 4th: (new: section 13.4 updated on Monday, May 28th) Do problems
- Chapter 13, Section 1: 1, 7, 11, 16, 19, 24, 28
- Chapter 13, Section 2: 1, 13, 16, 21, 30, 33, 37
- Chapter 13, Section 3: 5, 12, 16, 17, 19
- Chapter 13, Section 4: 5, 7, 8, 9, 19, 24
- Chapter 13, Section 5: 1, 2, 5, 8, 9, 17, 21, 26, 28
- Due Monday, June 11th: Do problems
- Chapter 14, Section 1: 9, 18,
31-36,39, 50 55, 62, 65 - Chapter 14, Section 2: 1, 9, 17, 27, 32, 41, 49, 56, 61
- Chapter 14, Section 3: 5, 22, 26, 39, 46, 54, 63, 65
- Chapter 14, Section 4:
3,7, 12, 14, 25, 31, 35, 50, 51 - Chapter 14, Section 5: 3, 8, 13, 21, 26, 29, 34, 35, 36, 39
- Chapter 14, Section 6: 3,
9, 15, 19, 24, 29, 33, 43, 47, 49, 54, 58 [part a only], 61, 65, 67 - Due Monday, June 18th: (last 3 sections added on Thursday, June 14th) Do problems
- Chapter 14, Section 3: 46, 54
- Chapter 14, Section 7: 2, 17, 27, 31, 41, 44, 55, 59
- Chapter 14, Section 8: 5, 10*, 11, 20, 29, 35 *Note for problem 10: the cylinder's surface area does not include the caps.
- Chapter 15, Section 1: 1, 14, 22, 27
- Chapter 15, Section 2: 19, 26, 35, 51, 57, 59
- Chapter 15, Section 3: 3, 16, 21
- Chapter 11, Section 3: 9, 36
- Chapter 15, Section 4: 1,3,5,7*,15,21,23,45,46 *Note for problem 7: to see why it is a circle, complete the square
- Chapter 15, Section 6: 1,6,12* *Note for problem 12: to clarify any ambiguity, it is the region with x values greater than 4y^2
- Due Monday, June 25th: Chapter 15, Sections 5-7 and Chapter 16, Sections 1-2. The problems for these sections are below.
- Future Homework and Practice problems (whatever isn't on the Monday, June 25th HW set will be for you to practice.)
- Chapter 15, Section 5: 3, 9,
21, 23, 33, 34, 39 - Chapter 15, Section 6: 29
- Chapter 15, Section 7: 1, 11, 14, 21, 31, 37,
41, 45, 55, 59, 65, 67, 69 - Chapter 16, Section 1:
9, 11, 14, 19, 22, 25 - Chapter 16, Section 2:
9, 19, 23, 29, 32, 34, 35 [part c only], 49 - ...
- Chapter 16, Section 3: 1, 2, 3, 5, 7, 10, 19, 29
- Chapter 16, Section 4: 2, 7, 9, 20, 23, 24, 25, 26
- Chapter 15, Section 8: 3, 7, 9, 23
- Chapter 9, Section 4: 1, 5, 14