<p>@Ren if you want to see a really good video on how to graph a polar curve, you can go to this site: [Just</a> Math Tutoring](<a href=“http://www.justmathtutoring.com%5DJust”>http://www.justmathtutoring.com) go to the “free calculus videos” link and find the thing that says “graphing a polar curve-part 1”</p>
<p>…i just tried to explain the limits thing but I realized I’m horrible at explaining, so I just erased it. sorry. </p>
<p>but the limits depend on the direction and order that the graph is being plotted. I do know that much. because sometimes it looks like its a positive radius and negative theta or something but really its a negative radius…</p>
<p>see, i told you i’m bad at explaining </p>
<p>i bet TheMathProf could do a better job? :)</p>
<p>To be honest, that’s the only thing I never learned. I never found a good place to cover that. Here’s a suggestion though.</p>
<p>I saw one of those question pop out in the Multiple Choice section.</p>
<p>3 out of the 5 answers weren’t in the form 1/2 r^2 dtheta, so you had 50% of getting it right. If you were even more astute, you could probably judge by the angle measures which will yield the bigger area, and thus if you want the smaller loop pick the other one.</p>
<p>I’m actually extremely rusty with these, but I’ll give it a stab:</p>
<p>In the problem that you’re working with, the appearance of the two loops is caused by the r value passing through 0 (the Cartesian point is (0,0)), and changing from either negative to positive or positive to negative. We want to find where these points occur, so we set r = 0. r = 0 when 1 + 2 cos @ = 0, which occurs when cos @ = -1/2, which occurs when @ = 2pi/3 and @ = 4pi/3.</p>
<p>By inspection, we can see that the smaller limacon occurs on the interval [2pi/3, 4pi/3], since on that interval |r| <= 1. So the area is given by:</p>
<p>Integral(1/2r^2 d@, where 2pi/3 <= @ <= 4pi/3 are your limits of integration)</p>
<p>^thanks. that’s the same answer as the book by the way.
so the method is pretty much looking at the picture, then set r = 0?</p>
<p>U VA, hm… i watch alot of patrickJMT’s vids on calculus in youtube; when i looked up polar graphs back then, i thought he’s only showing us how to graph it, so i didn’t bother to look at them. lol. i will look at them now~~ kinda iffy on the graphing part too…</p>
<p>=D meh,im jumping topics lol. i was studying some taylor series earlier, then jumped to some convergence tests… then lagrange bound, now polars… lol…im crazy =/
oh yeah guys, are u doing all the FRQ fro BC from the CB? Those are definitely helpful. im pretty sure i’m going to get a 5 after i finish all of them. lol… try them out if yall havnt!</p>
<p>^I would just, I’m just too occupied with Mu Alpha Theta currently.</p>
<p>The BC Topic test is about 5x harder than the BC Exam, so…yeah. They have some crazy questions sometimes. It’s all based on shortcuts as well. There was one that was like, find 15th derivative of arctan x at x = 0. Of course, there is no “nth” derivative for arctan , so good luck with that. There’s a very nice shortcut though. Props if you see get it.</p>
<p>Personally, prepping for MAO > prepping for AP. I’ll probably take like a test or two a week before the exam, just so I know how the test will go, then try some of the long response.</p>
<p>A calculator (the pocketkind) might not be able to evaluate 2004!/2003!. It also helps build certain ideas. It helps you think different. Without knowing how to add, and the likes, it’d be impossible to think of the things we think of. </p>
<p>It’s also more practical when it comes to day-to-day things. However, evaluating the integral of sin e^x from pi to 3pi/29 is not exactly something worth doing over.</p>
<p>Now mind you, adding and subtracting sure helps for creating new theorems, and exploring the realm where numbers are just variables, but when applications comes into play, a calculator is simply better.</p>
<p>Also, it is quicker to be able to multiply, add, etc. in your head than punching everything into a calculator, whereas it is quicker to find an integral with a calculator than doing it by hand. (in most situations)</p>
<p>and leaving the “real world” behind for a moment…the exam is timed.</p>
<p>I’m not saying that you guys shouldn’t use a calculator on the AP exams; I just think that <opinion> the AP calc curriculum shouldn’t include calculators </opinion> …</p>
<p>well of course you’re entitled to your opinion, but I actually think it works pretty well how it is with half and half so we learn how to do both
oh and I thought of something else…i assume they are able to include more difficult problems that couldn’t be solved by hand in such a limited amount of time?
okiedoke. that’s the end of my take on this :)</p>
</p>
I knew you could give an explanation that made sense <em>cheers for TheMathProf</em></p>