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)
  
  
  • Biography and portraits of Sir Isaac Newton (1643-1727)
  • Wikipedia biography and portrait of Sir Isaac Newton (1643-1727)
  
  
  • Biography and portraits of Gottfried Wilhelm von Leibniz (1646-1716)
  • Wikipedia biography and portrait of Gottfried Wilhelm von Leibniz (1646-1716)
  
  
• 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