CHS Calculus

Test

2009-03-12T13:03:00.000-07:00

Here is the first part of your test. It is to be completed outside of class and is due Monday morning (3/16). We will have the second part of the test either tomorrow or Tuesday depending on the weather.

2009-03-12T11:30:00.001-07:00

Here is a link to some algebra review (the same simplifying of exponents that we were doing today)
If you want some practice its a good place to start.

http://www.algebasics.com/3way6.html

2009-03-02T21:05:00.000-08:00

All right. Here's the deal. Sorry I blew my top at you all last Friday. Most of you all are doing really well...and the rest of you just need to spend more time with the material. And that's really the bottom line. Every one of you gets how to do these integrals as soon as you are reminded of the rules and methods but you need to spend time engaging with the problems by yourself if you are ever really going to "own" the material.

So like I said here's the deal. We are going to have a test just on the integrals this Friday, I figure that's enough without adding the stuff on summation notation. I have given you solutions to the worksheets I handed out last week (see my last post) so that'll give you something to practice. Also, you'll find links below to webpages that have tutorials and problems for each of the integration techniques we have studied. Another perspective is always useful and also the problems break down the process and give you instant feedback which can be very helpful. You're assignment for tomorrow: (actually today, its getting late!) is to spend some time looking at each of theses pages and working these problems. This applies to all of you -- even if you feel like you have a good handle on the material. There will be a quiz at the beginning of class on Thursday drawn from these pages. As always, skip over problems that use rules we haven't studied (sec, tan, arcsin, etc.)

So, spend an hour or so with calculus, then enjoy your extra super long weekend...and no, you're not too old to play in the snow!

basic antiderivatives:
- (this has a review of everything but "by-parts" and so might come in really hany when studying for test...for the quiz on Thursday be sure to click on the "problem sets" link in the antiderivative section)
  
  http://www.qcalculus.com/cal09.ht
u-substitution:
- http://people.hofstra.edu/Stefan_Waner/RealWorld/tutorials4/frames6_2.html
- (These are some examples if you need extra help. This won't be part of the quiz. There are drill problems though with solutions...this is a great way to study for the test on friday...hint,hint)
  
  http://archives.math.utk.edu/visual.calculus/4/substitutions.3/index.html
  **
integration by parts:
- http://archives.math.utk.edu/visual.calculus/4/int_by_parts.3/**

** the solutions to these examples refers to a "Table of indefinite integrals" here's a link to it for you. Consider it your online version of the "hand-dandy integral table." Rules 1-6 are the ones we've covered together.

Solutions

2009-03-02T20:50:00.000-08:00

Here are the solutions I've promised. Stayed tuned...I'll let you know what we'll be up to in the next couple of classes in my next post. (btw the strange symbol in #12 of the first set is actually supposed to be a two...not sure why it came out that way)

Precalculus Assignment 1/29

2009-01-29T10:26:00.000-08:00

First, make sure you've finnished the home work I assigned Friday (that is to make up your own "variation" problem like the ones we've been working on in class -- thanks for sending me yours Isha)

Next I have a challenge for you. I want you to think about the following:

a) f(x)=f(-x)
b) f(x)=-f(-x)
c) f(x)=f(x+5)

The first two you should find something like in your note from the past week. The last you haven't seen before.

In each case you are given some information about a function (assume its a different function in each case). You are not told exactly what the function is, just given some information about it. What I want you to do is think about how each function might look when graphed...again, you can't know specifically, but the information you are given does tell you something important about the picture in each case. Your task is to draw the graph of a function that might fit the info given in each case (so you'll have three graphs). As I have said the first two you should find in your notes. The last is a challenge.

1/29 Calculus Assignment

2009-01-29T09:27:00.000-08:00

(Click on the images...the bigger version is still fuzzy, but its legible.)

Ok folks...please review your notes on"u-substitution." Remember this is the "backwards" chain rule. Here is an example:

Its a pretty easy example. Here is a tricky one:

Your task is to come up with most difficult "u-substitution" problem that you can. I suggest you start with a chain rule derivative problem then obfuscate it (cool word, look it up if its unfamiliar). Some hints on making it tricky: rearrange the terms, multiply by constants. See my example above.

Homework: Due Tuesday 1/20

2009-01-16T09:37:00.000-08:00

Class notes from 1/9

2009-01-13T06:50:00.000-08:00

Sorry about the funky picture quality...also the color in the pictures came out strangely. I'll see what I can do to make it better in the future. Here is a link to more information on "summation notation." Even if you're not confused, check it out. Learning is good!

solutions1_6

2009-01-08T17:50:00.001-08:00

Solutions for work assigned on 1/6/2009
Oil Spill
1.

2. You can do this in several different ways: If you choose the flow rate at the beginning of each hour to calculate the oil spilled in that hour you should get 2140 gallons. This method is illustrated in the graph above

3. By my method I over estimate how much oil spills. For the first few hours and the last few, the estimate is pretty good. In the middle, the flow rate drops very quickly so my estimate is pretty bad (make sure you understand why this is so).
4. Mid-hour flow rates, especially for the middle group of hours.

Can the car stop in time?
1. Calculate the minimum distance by using the speed at the end of each 2s interval to calculate the distance during that interval. You should get 184 ft.
2. Calculate the maximum distance by using the speed at the Beginning of each 2s interval to calculate the distance during that interval. You should get 304 ft.
3. Probably. The maximum estimate on the distance traveled doesn't miss the deer but it comes close. The actual distance traveled probably does miss the deer.
4. Calculate the maximum estimate on the distance traveled...you should find its less than 300 so the driver does miss the deer.

The blue line is the plot of the data
given, the red line represents the
maximum estimate and the yellow
line, the maximum estimate.