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). See the grading policies for general instructions on doing homework and how it will be graded.

Introduction and Review:
- Date assigned: January 8 Wednesday.
- Date due: January 10 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.
Work:
- Date assigned: January 9 Thursday.
- Date due: January 14 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 15 Wednesday.
- Date due: January 21 Tuesday.
- 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 16 Thursday.
- Date due: January 23 Thursday.
- 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: 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 23 Thursday.
- Date due: January 28 Tuesday.
- 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 28 Tuesday.
- Date due: January 31 Friday.
- 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 29 Wednesday.
- Date due: February 3 Monday.
- Problems from §8.5 (pages 460&461): No additional work needed: 10, 14, 16, 20, 30, 34.
Numerical integration:
- Date assigned: February 3 Monday.
- Date due: February 6 Thursday.
- 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 Tuesday.
- Date due: February 10 Monday.
- 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 10 Monday.
- Date due: February 12 Wednesday.
- 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 11 Tuesday.
- Date due: February 14 Friday.
- Problems from §9.2 (pages 505&506):
  - No additional work needed: 3, 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 necessary (but be sure to do everything in the instructions): 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.a&b, 82;
  - Extra credit (turn in individually): 88;
  - Show what finite equation you solve: 90.
Telescoping series:
- Date assigned: February 13 Thursday.
- Date due: February 18 Tuesday.
- Problems from §9.2 (pages 505&506):
  - No additional work needed: 5, 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 necessary (but be sure to do everything in the instructions): 51, 55, 61, 62, 65, 81.c.
The Integral Test:
- Date assigned: February 17 Monday.
- Date due: February 20 Thursday.
- 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 19 Wednesday.
- Date due: February 24 Monday.
- 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, how what series you compare to: 19, 21, 22, 25, 27, 29, 32, 33, 34, 37, 45, 47, 51.
More convergence tests:
- Date assigned: February 21 Friday.
- Date due: February 28 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: 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: 56, 59, 61;
  - Show the limit of the ratios and the limit of the roots: 63.
- 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;
  - Show your numerical calculation: 49, 51;
  - State at least the number of terms that you use: 57.
Absolute convergence:
- Date assigned: February 25 Tuesday.
- Date due: March 3 Monday.
- Problems from §9.6 (pages 527&528): 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.
Power series:
- Date assigned: February 27 Thursday.
- Date due: March 4 Tuesday.
- 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, 29, 31;
  - Show what limit you take: 39.
Taylor series:
- Date assigned: March 5 Wednesday.
- Date due: March 7 Friday.
- Problems from §9.7 (pages 536–538): 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.
- 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;
  - Show what numerical calculations you make or what equations or inequalities you solve: 37, 39, 41, 48.
Parametrized curves:
- Date assigned: March 6 Thursday.
- Date due: March 11 Tuesday.
- 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.
Calculus with parametrized curves:
- Date assigned: March 11 Tuesday.
- Date due: March 13 Thursday.
- 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 12 Wednesday.
- Date due: March 20 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 14 Friday.
- Date due: Never.
- 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 at least two intermediate steps: 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;
  - Show at least one intermediate step for part c: 31;
  - Show at least one intermediate step: 34, 35;
  - Show what numerical calculations you make or what equations you solve: 42, 47.
- 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.

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