Precalculus Assignment 1/29

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

(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

Class notes from 1/9

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

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.