Homework

In case you miss a homework assignment in class, you can find it below. Unless otherwise specified, all problems are from the 2nd Edition of University Calculus: Early Transcendentals published by Addison Wesley (Pearson). When I return graded homework, I may post some solutions here too; see the downloading help if you have trouble reading them. See the grading policies for general instructions on doing homework and how it will be graded.

Introduction and review:
- Date assigned: January 7 Wednesday.
- Date due: January 9 Friday.
- Problems from §5 Practice Exercises (pages 345–348):
  - Show at least one intermediate step for each part: 9;
  - Show at least one step before and after performing a substitution: 45, 51, 55, 65;
  - Show at least what numerical calculation you make: 73, 75, 77, 85, 87, 95, 105;
  - No additional work needed: 121;
  - Show at least one intermediate step: 125.
- Extra credit (essay): Explain your background in mathematics and what you are going to use this course for.
- Some answers: DejaVu format, PDF format.
Work:
- Date assigned: January 9 Friday.
- Date due: January 13 Tuesday.
- Problems from §6.5 (pages 386–389):
  - For each result, show what numerical calculation you make or what direct integral you evaluate: 5, 8, 9, 11, 13, 15, 16, 21;
  - Show at least two intermediate steps: 23;
  - Show what numerical calculation you make using kinetic energy: 25.
Moments:
- Date assigned: January 13 Tuesday.
- Date due: January 15 Thursday.
- Problems from §6.6 (pages 396&397): Show what definite integrals you evaluate: 3, 6, 7, 11, 13, 15, 25.
Differential equations:
- Date assigned: January 15 Thursday.
- Date due: January 20 Tuesday.
- Problems from §7.2 (pages 418–420):
  - Show y′ (meaning dy/dx) as an intermediate step: 3, 6, 7;
  - Show what integrals you take after separating variables, and be sure to solve for y (which the answers in the back do not finish, except for #17): 11, 13, 17, 18, 21;
  - Show what equation (differential or otherwise) you solve or what numerical calculation you make: 33, 35, 36, 39.
Integration by parts:
- Date assigned: January 20 Tuesday.
- Date due: January 22 Thursday.
- Problems from §8.1 (pages 436–438): Show at least u, du, v, and dv for each integration by parts: 3, 6, 11, 17, 18, 25, 41, 47, 49, 61, 64, 67.
Advanced integration techniques:
- Date assigned: January 26 Monday.
- Date due: January 28 Wednesday.
- Problems from §8.2 (pages 443&444): Show at least one intermediate step showing the integral after all trigonometric identities have been applied: 11, 19, 35.
- Problems from §8.3 (pages 447&448):
  - Show at least one intermediate step showing the integral after all trigonometric substitutions have been applied: 5, 11, 17;
  - For each part, show at least one intermediate step showing the integral after all substitutions have been applied: 57.
- Problems from §8.4 (pages 454&455): Show at least one intermediate step showing the integral after all fractions have been parted: 11, 17, 27.
Analytic integration using computers and tables:
- Date assigned: January 28 Wednesday.
- Date due: January 30 Friday.
- Problems from §8.5 (pages 460&461): No additional work needed: 10, 14, 16, 20, 30, 34.
Numerical integration:
- Date assigned: January 30 Friday.
- Date due: February 6 Friday.
- Problems from §8.6 (pages 468–470): Show what numerical calculations you make: 5, 7, 15, 17, 23, 27.
Improper integrals:
- Date assigned: February 4 Wednesday.
- Date due: February 6 Friday.
- Problems from §8.7 (pages 479–481): Show at least what limits you evaluate: 3, 9, 14, 17, 19, 31.
Infinite sequences:
- Date assigned: February 6 Friday.
- Date due: February 10 Tuesday.
- Problems from §9.1 (pages 495–498):
  - Show what numerical calculation you make to find each term: 1, 3, 5, 9, 12;
  - No additional work needed: 15, 21, 22, 23;
  - Show at least one intermediate step for each limit, or give a reason for divergence: 27, 35, 37, 38, 41, 43, 45, 48, 51, 53, 55, 60, 66, 73, 83;
  - Show what numerical calculation you make to find each term: 99.
Infinite series:
- Date assigned: February 10 Tuesday.
- Date due: February 12 Thursday.
- Problems from §9.2 (pages 505&506):
  - No additional work needed: 3, 5, 9, 12, 13;
  - Show a formula for the partial sums or show a calculation using a formula for the sum of a geometric series: 15, 17, 18;
  - Show the limit of the terms: 27, 31, 32;
  - No additional work needed: 35, 37, 40;
  - Show a formula for the partial sums or show a calculation using a formula for the sum of a telescoping series: 43, 46;
  - No additional work needed (but be sure to do everything in the instructions): 51, 55, 61, 62, 65, 69;
  - Show a formula for the partial sums or show a calculation using a formula for the sum of a geometric series: 73;
  - No additional work necessary: 81, 82;
  - Extra credit (turn in individually): 88;
  - Show what finite equation you solve: 90.
The Integral Test:
- Date assigned: February 12 Thursday.
- Date due: February 16 Monday.
- Problems from §9.3 (pages 511&512):
  - Write down what integral you check; also note at what point (if not immediately) the Integral Test applies: 3, 9;
  - State at least which test you are using: 13, 16, 19, 21, 25, 28, 29, 31, 33, 35, 37.
Comparison tests:
- Date assigned: February 16 Monday.
- Date due: February 18 Wednesday.
- Problems from §8.7 (pages 479–481): Show what integrals you compare to, and indicate whether the comparison is direct or in the limit: 41, 43, 45, 53, 59.
- Problems from §9.4 (pages 516&517):
  - Show what series you compare to, and show which inequality holds between the two series (and for which terms, if not all of them): 5, 6;
  - Show what series you compare to, and show the limit of the ratio of the two series: 10, 14;
  - State at least which test you are using; in the case of a comparison test, show what series you compare to: 19, 21, 22, 25, 27, 29, 32, 33, 34, 37, 45, 47, 51.
The Ratio and Root Tests:
- Date assigned: February 18 Wednesday.
- Date due: February 20 Friday.
- Problems from §9.5 (pages 521&522):
  - Show the limit of the ratios: 1;
  - Show the limit of the roots: 9;
  - State at least which test you are using (and state what series you compare to if you use a comparison test): 17, 21, 23, 24, 25, 29, 33, 34, 35, 41;
  - Use the Ratio Test, and show the limit of the ratios: 47, 51;
  - State at least which test you are using (and state what series you compare to if you use a comparison test): 56, 59, 61;
  - Show the limit of the ratios and the limit of the roots: 63.
Series with negative terms:
- Date assigned: February 20 Friday.
- Date due: February 24 Tuesday.
- Problems from §9.6 (pages 527&528):
  - Show the limit of the terms (or of their absolute values); if the series converges, state when its terms' absolute values begin decreasing (if not immediately): 1, 9, 10, 12, 13;
  - State at least which test or tests you use (you may need two for some of these): 17, 21, 22, 27, 29, 30, 33, 35, 37, 39, 40, 43;
  - Show your numerical calculation: 49, 51;
  - State at least the number of terms that you use: 57.
Power series:
- Date assigned: February 24 Tuesday.
- Date due: February 26 Thursday.
- Problems from §9.7 (pages 536–538):
  - Show what limit you take to find the radius of convergence, and state at least what tests you use to treat the endpoints (if any) of the interval of convergence: 5, 7, 8, 15, 17, 18, 23, 31;
  - Show what limit you take: 39.
  - Show what calculations you make (if any) to find the radii of convergence, show a formula for the sum of a geometric series to calculate the sum of the series, and show at least one intermediate step for the sum of the derivative series: 49.
Taylor series:
- Date assigned: February 26 Thursday.
- Date due: March 2 Monday.
- Problems from §9.8 (pages 542&543):
  - Show at least the values of the relevant derivatives at a: 1–9 odd;
  - Either show enough derivatives that the pattern is clear or show substitution into a formula given in the textbook: 11, 13, 14, 15, 17, 23, 27.
- Problems from §9.9 (pages 549&550): Either show enough derivatives that the pattern is clear or show substitution into a formula given in the textbook: 1, 5, 11, 12, 17, 21, 22.
More with Taylor series:
- Date assigned: March 3 Tuesday.
- Date due: March 5 Thursday.
- Problems from §9.9 (pages 549&550): Show what numerical calculations you make or what equations or inequalities you solve: 37, 39, 41, 48.
- Problems from §9.10 (pages 556–558):
  - Show at least one intermediate step for each: 3, 5, 7, 12, 13;
  - Show at least what equations or inequalities you solve or what numerical calculations you make, to determine the number of terms to use or to check that you have enough terms: 25, 27;
  - Show at least one intermediate step for each: 29, 31, 33, 59, 61, 71.
Parametrized curves:
- Date assigned: March 5 Thursday.
- Date due: March 9 Monday.
- Problems from §10.1 (pages 568–570):
  - Show at least one intermediate step on the way to finding the cartesian equation: 5, 7, 13;
  - Show at least one intermediate step of algebra: 23;
  - Show at least one intermediate step (besides the hint) for each variable (hint: tan θ = y/x): 31.
- Problems from §10.2 (pages 577–579):
  - Show what differentials or derivatives you find along the way: 1, 13, 19;
  - Show what integrals in t you take: 25, 29.
Polar coordinates:
- Date assigned: March 9 Monday.
- Date due: March 12 Thursday.
- Problems from §10.3 (pages 582&583):
  - No additional work needed: 1–4;
  - Show what numerical calculations you make: 5, 6, 9;
  - Show at least one intermediate step of algebra for each: 27, 31, 45, 50.
  - Problems from §10.4 (pages 586&587):
    - No additional work needed: 3, 7, 8, 9, 13, 16;
    - Show what derivatives or differentials you take: 17, 19;
    - No additional work needed: 21–24.a, 25.
  - Problems from §10.5 (pages 590&591): Show what integrals (in one variable) you take: 21, 25, 27.
Graphs and vectors in three dimensions:
- Date assigned: March 12 Thursday.
- Date due: March 16 Monday.
- Problems from §11.1 (pages 605&606):
  - No additional work needed: 1, 3, 7, 8, 11, 19, 25, 29, 30, 35, 37, 39;
  - Show what numerical calculation you make or what equation you solve: 41, 45;
  - No additional work needed: 49, 51, 52;
  - Show at least two intermediate steps: 57;
  - No additional work needed: 59;
  - Show what numerical calculations you make or what equations you solve: 62.
- Problems from §11.2 (pages 614–616):
  - Show at least one intermediate step for each part: 3, 7, 8, 11, 13, 15, 18, 19;
  - Show also u, v, and w as appropriate in each picture: 23;
  - No additional work needed: 31, 34;
  - Show at least one intermediate step for each part: 35;
  - Show what numerical calculations you make or what equations you solve: 42, 47.
Multiplying vectors:
- Date assigned: March 16 Monday.
- Date due: March 19 Thursday.
- Problems from §11.3 (pages 622–624):
  - Show at least one intermediate step for each result: 1, 5, 7, 8;
  - Show what numerical calculations you make or what equations you solve; you may leave exact answers involving trigonometric operations: 10, 11, 23;
  - Show at least a formula for each slope: 31, 32;
  - Show what numerical calculations you make or what equations you solve: 35, 37.
- Problems from §11.4 (pages 628–630):
  - Show what numerical calculations you make: 3, 6, 11, 12, 17, 20, 21, 23;
  - No additional work needed: 27, 28, 29, 31;
  - Show what numerical calculations you make: 35, 38, 39, 43.
Geometry with vectors:
- Date assigned: March 19 Thursday.
- Date due: Never.
- Problems from §11.5 (pages 636–638): 3, 7, 8, 11, 13, 15, 18, 19, 23, 31, 34, 35, 42, 47.

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