Chapter 2: Limits and Derivatives
Class Notes
- 2.1 The Tangent and Velocity Problems (pdf)
- 2.2 The Limit of a Function (pdf)
- 2.3 Calculating Limits Using the Limit Laws (pdf)
- 2.4 Continuity (pdf)
- 2.5 Limits Involving Infinity (pdf)
- 2.6 Tangents, Velocities, and Other Rates of Change (pdf)
- 2.7 Derivatives (pdf)
- 2.8 The Derivative as a Function (pdf)
- 2.9 What Does f' Say about f? (pdf)
- Review of Chapter 2 (pdf)
Homework
- 2.1 -- 1 (tank), 3, 5 (ball), 7 (cyclist)
- 2.2 -- 1, 3, 7, 8 (injection), 15, 17, 23 (estimate a limit), 27 (how close?)
- 2.3 -- 1, 2, 5, 8, 13, 17, 23, 25 (squeeze theorem), 31, 40 (Lorentz contraction)
- 2.4 -- 1, 2, 3, 7, 8, 11, 12, 15, 21, 31, 36 (Intermediate Value Theorem), 37, 41 (real root)
- 2.5 -- 1, 3, 7, 13, 17, 21, 25, 34 (asymptotes), 39 (horizontal asymptote), 46 (relativity), 47 (brine tank), 49 (how large?)
- 2.6 -- 1, 3, 5, 9, 15 (car), 18 (arrow on the moon), 20, 24 (population of Canada), 26 (coffeehouses), 28 (tank)
- 2.7 -- 1, 2, 3, 4, 7, 9 (equation of tangent line), 15, 21, 23, 27 (cost of mining), 29 (fuel consumption), 31 (temperature in Dallas), 34 (salmon)
- 2.8 -- 1, 3, 12 (yeast population), 17, 23, 29 (unemployment), 31, 37, 39, 41(derivatives), 47 (not differentiable)
- 2.9 -- 1, 3, 5 (national deficit), 6 (yeast cells), 9 (gaining knowledge), 10 (coffee mug), 17, 23 (behaviour of a function)
Review
Use the following exercises to review and test your understanding of the material in Chapter 2. This is not homework, and there is nothing to hand in from this activity.
- Review Exercises, Chapter 2, pp. 176--178 -- 1, 3, 7, 11, 18, 21, 24, 25, 27, 37, 38, 39, 40, 41
Mathematica Notebooks
The following Mathematica notebooks are available in two formats. Download the Mathematica notebooks (nb) to your machine and use Mathematica to interpret their contents, or click on the web page link (html) to see a static image of the evaluated notebook.
- 2.1 The Tangent and Velocity Problems nb
html
- 2.2 The Limit of a Function nb
html
- 2.3 Calculating Limits Using the Limit Laws nb
html
- 2.4 Continuity nb
html
- 2.5 Limits Involving Infinity nb
html
- 2.6 Tangents, Velocities, and Other Rates of Change nb
html
- 2.7 Derivatives nb
html
- 2.8 The Derivative as a Function nb
html
- 2.9 Linear Approximations nb
html
- 2.10 What Does f' Say about f? nb
html
Lab Projects
These projects explore a number of the techniques, concepts, and applications of calculus. Use your browser to view the project instructions (pdf), the data set descriptions (data sets), and the html versions of other files. Download the Mathematica notebooks (nb) and Excel spreadsheets (xls) to your own machine, and open them with those applications.
- 2.6 Interpolation and Extrapolation pdf
cparrish@sewanee.edu