Welcome to **Calculus**!

graph match - big derivative puzzle

The idea is to look at the properties of amount functions (e.g. \(f(x)\)) and their rate functions (the derivative functions, e.g. \(f'(x)\)).

*A note on the puzzle:*

You can make the puzzle task more interesting by scrolling the browser to hide the true/false hints.Building a rate function Using the slope of tangents

- Kwikis (just below current homework)

**Homwork Sources:**

**Next Test:** Wed October 4 (generally every other Wednesday)

Due Date | Assignment |
---|---|

Tue 8/22 | * Sign Up for WeBWork * TurnIn: Observations Please * Though you will need to be have and know how to use a hand held graphing calculator (e.g. TI-84) for the AP exam, you will find the Demos Graphing Calculator which runs on computers, smart phones, and tablets, to be very useful. Start by trying it on a computer. You can save your work if you click sign-in in the upper left hand corner of the window.* Work through this brief introduction to graphing functions in Desmos. |

Wed 8/23 | Turn In: Second draft of Headlands Bicycle problem on page 2 of kwiki 20002 Note that you may need to make an assumption about my ride to get a unique solution for flat, uphill, and downhill miles. Be sure to state your assumption. * Spend 30 minutes working on the questions. * Then spend 15 minutes writing a second draft of your answers and graphs. * I do not want to see your initial work. Use new paper for your second draft. |

Thu 8/24 | * Read Whitman section 1.3 Functions * Do exercises 13, 14, 15, 16 * Be prepared to talk about kwiki 20003 questions 4, 5, and 6. |

Fri 8/25 | * WeBWork: “Orientation” Your login is all lower case lastname_firstname e.g. newton_isaac using the names you entered. Although the closing time is midnight Sunday, I expect you to spend 45 minutes (or less) to work your way through this orientation tonight.* Precalc Quiz: 30 minutes, 2 free response questions. |

Mon 8/28 | * Consider what you learned your first week of your journey through Calculus. You should talk about amount functions, rate functions, locally linear, and our seven easy pieces of “nice” function curves. Your tasks are to create two documents that will help students learn about these concepts.1. Building Rate Functions: Take a look at this mathlet - Building a Rate Function. The mathlet needs user guide: — (a) a set of instructions how to use the buttons, boxes, etc.; and — (b) a paragraph explaining how \(f'(x)\) is defined and what \(f'(x)\) means. Be sure to explain and use the concepts of amount functions, rate functions, and locally linear. 2. Using Rate Functions: Make nice version of the Seven Easy Pieces table (see kwiki 20005 question 1) and write a paragraph describing what the table says. TurnIn: in typed second drafts of your work for tasks 1 and 2. (You can handwrite parts that might be difficult for you to do with a computer.)* (For a few of you who haven’t finished WeBWork: “Orientation”, it closes Sunday evening.) |

Tue 8/29 | * Review HMC Functions and Transformations of Functions * Start and Finish WeBWork: “New Functions from Old” * You might take a look at my interactive diagram from today’s slopes question. |

Wed 8/30 | * TurnIn: Redo questions 1 and 2 of today’s kwiki.— Briefly explain why each answer is correct. — Sketch the requested graph of \(f'\) on the graph of \(f\). — Sketch the requested graph of \(g\) on the graph of \(g'\). * Take another careful look at Building a rate function |

Thu 8/31 | * WeBWork: “Exponential Functions” * Put the difference quotient equation \[ f'(a) = \lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}\] on a PostIt. Place this PostIt on your bathroom mirror. * Take a look at Geometry of a Difference Quotient. * Your notes should include the concepts of stationary and critical points, and our definition of \(e\). |

Fri 9/1 | * WeBWork: “Inverse Functions and Logarithms” Pls attempt to finish this WeBWorK assignment tonight (but stop after 45 minutes if you are not done.) — Exponential and Log Functions is a brief review. * Check your understanding of seven easy pieces with graph match - big derivative puzzle (described at Places to Visit) * Use Looking at \(b^x\) at (0,1) to approximate the value of \(b\) that gives a graph tangent to \(y=x+1\) |

Tue 9/5 | * WeBWork: “Chapter 1 Review” * Use Looking at \(b^x\) at (0,1) to approximate the value of \(b\) that gives a graph tangent to \(y=x+1\) * HeadsUp: Test on Wednesday |

Wed 9/6 | Test (No calculators) |

Thu 9/7 | * Actively read HWS Intro to Limits. * WeBWork: “bic Limit of a Function” (one night only) |

Fri 9/8 | * Review One sided limits and Limit Properties * WeBWork: “bic Calculating Limits Using the Limit Laws” |

Mon 9/11 | An Important Trig Limit * Work on a first draft of your solution to evaluating \[\lim_{\theta \rightarrow 0^{+}}
\frac{\sin \theta}{\theta}\] See Kwiki 20011 Note: The kwiki question is structured to get you to think about the problem. Your solution need not be organized to mirror my kwiki questions.* TurnIn: a typed second draft of a complete write-up. Be sure to include at least one diagram. A complete write-up has a title and four labeled sections: __ Problem a full statement of problem __ Game Plan a summary of your approach __ Solution __ Final Thoughts comments about the problem and/or your solution |

Tue 9/12 | * Read at least first page of Continuity Notes * WeBWork: “bic-Continuity” * Bring your graphing calculator to class. |

Wed 9/13 | * WeBWork: “Shrinking Circle Problem” TurnIn: An organized second draft write-up of your work on this problem. This can be neatly handwritten. Note: If you do not solve the problem, come up with a question whose answer would help you get to a solution. |

Thu 9/14 | * Carefully read Adjectives for Functions * Do exercises 1, 2, 4, 5, 6 (on last page). Be sure to bring your Calculus notebook to class so that I can see your work. * Be prepared to discuss any of the problems on Kwiki 20014 by writing responses in your notebook. * Take a careful look at my sample write-up |

Fri 9/15 | * Be prepared to discuss all problems on the back of Kwiki 20015 by writing responses in your notebook. * TurnIn: A second draft of complete write-up for question 3: \(\bullet\) \(f(x)\) even and differentiable \(\implies f'(x)\) odd Consider why this statement is true by looking at the geometry behind the \(h \rightarrow 0\) difference quotient. Draw a good diagram labeling the relevant points. [Hint: Start with just two points in the first quadrant.] (Take a careful look at my sample write-up) |

Mon 9/18 | TurnIn: a Poster for WeBWork: “bic-alien-headlight”— Solve the problem. A graphing calculator or Desmos might help, but guess and check is not an acceptable method.— Plan a poster presentation of your solution using the standard write-up format. — Use Desmos to make a diagram. — Use one piece of standard \(8.5 \times 11\) paper. |

Tue 9/19 | * Second Derivative Exercises #1,2,4,6 * ReCheck your understanding of seven easy pieces with graph match - big derivative puzzle (described at Places to Visit)* Start reviewing for Wednesday’s Test. |

Wed 9/20 | Test |

Fri 9/22 | Do Derivative Rules 1 worksheet twice. Use stratch paper (or another copy of this worksheet) for your first drafts. Neatly write your second drafts on the worksheet, and bring it to class. |

Mon 9/25 | * Read and Do exercises for Derivative Short Cuts - Power Rule Sec 3.1 #1,3,4,5; sec 3.2 #1-5(all) 7,9 * Make a Desmos graph of \(f(x)=ax^2+bx+c\). ___ Use sliders for the parameters (\(a\), \(b\), and \(c\)) to explore what each parameter does. ___ Save your file, because you will be doing more with it Monday. |

- Kwiki 20017 \(\displaystyle \frac{\sin 0}{0}\) redux, IVT, hiker problem

- Kwiki 20011 An important trig limit
- Kwiki 20012 defining
*continuous*with limits, using the cheer, difference quotients, exponential functions, - Kwiki 20013 graphing calculator and a discontinuity, from yesterday
- Kwiki 20014
- Kwiki 20015 introduced
*Taylor Form*of a line, logs - Kwiki 20016 from yesterday, \(\displaystyle \frac{\sin 0}{0}\) redux

- Kwiki 20001 slope, attributes of graphs
- Kwiki 20002 dividing by zero, attributes of graphs
- Kwiki 20003 functions, amount functions and rate functions, tangents, seven easy pieces (part I), composite functions, rational numbers
- Kwiki 20004 functions, amount functions and rate functions, composite functions, rational numbers, seven easy pieces (part II),
- Kwiki 20005 seven easy pieces (part II)
- Kwiki 20006 using seven easy pieces
- Kwiki 20007 \(f\) \(f'\) match
- Kwiki 20008 Odd and Even functions, Using a difference quotient on \(f(x)=b^x\).
- Kwiki 20009 Odd and Even functions, logs and exponents
- Kwiki 20010 Review questions, limits using graphs of functions

Please read this entire page. Be sure to Sign Up for WeBWork before 7am Tuesday, August 22.

We are using:

Whitman Calculus, an open source text book. You can read it on-line Whitman online, download to any device that can show

*PDF*s, or print selected pages.

Copies of Stewart

**Calculus**are available if you want to read a Calculus text with worked examples.

As in previous math clases some homework assignments will come from the [Whitman Calculus] text, but other assignments will be done on-line using WeBWorK , an on-line math homework system.

You need to fill out this form To get a set up an *WeBWorK* account. Be prepared to give a (and remember) a password for your account. (Yes, the submit button says “Never submit passwords through Google Forms.” Your WeBWorK password is not a high level security item.) Details about using *WeBWorK* will be available soon. If you can't wait, you can sign-in as a *guest*.

- Bring your calculator to class starting Monday, August 29.
- For most of you, here are basics of TI-83, notes on using the TI-83/4 (a pdf file), and/or a TI-83/84 On-Line Tutorial. This might also help.
- For the computing hungry, here are basics of TI-89, notes on using the TI-89 (a pdf file), and/or a TI-89 On-Line Tutorial
- And if you have been given a free TI-86, here is a TI-86 On-Line Tutorial