Post 35

Ok I'll go over a few things I've learned this week about the free response sections of the ap (although today is Wednesday and the blogs were due Sunday).

Some things I learned include how to find bounds on an integral of area or volume when the bounds are not already given using the intersection function on your calculator, that a chart (although I hate them) on the free response portion of the ap is the best and easiest problem to have, that there is another way to do trapezoid rheeman's sum when using a chart, that RATE is not a derivative, it is an integral, and that you will always have to find the slope for part a of these problems.

Ok, first things first, how to find bounds when they are not given. Most of the time these problems will be shown on the calculator portion unless the bounds are clearly stated. Before, I just skipped these problems because I didn't know how to find them and when I did figure out how to find them I completley could not decide whether I wanted to use the x point or the y point for my bounds. But now I have all of this straight, so I will share it with you all. Here are the steps

1. Plug your function(s) into y=
For this, you'll either have two equations that will intersect or one equation that will intersect with either the x or y axis. A point of intersection is just what you want

2. After you plugged your function(s) into y=, you can graph them and find your intersection points. To do this hit 2nd, calc, intersect, enter. The function will guide you to locate your first line, then your second line, then your guess. After this it will give you your point. Always use the x point for this unless you are rotating about the y axis. Make sure you find all your points of intersection that connect to either the area or the volume you are rotating for your bounds.

So the chart problems are supposibly the easiest parts on the ap. I still get them wron all the time, ha. Part a will always ask you for a slope (even though it may say something else) always take the slope.

If you forgot (I did) Rheeman sums are really just finding the area of something. Another way to do a trapezoid rule is this:
(b1-b2/2)(h)
This is the first base minus the second base divided by 2 times the height. You'll add these all together and divide by your subinterval to find your answer.

I don't really remember optimization. I'll need help on this considering I'll need to do my prob/stats project on something relating to it.

Thanks.