<p>@dchau503 yes logistic functions grow fatest at half the carrying capacity. It’s one of those things that’s really easy as long as you know it.</p>
<p>Sooo I did really well in Calc BC this year but I’ve seemed to have forgotten lots of it and the exam is in 3 days…yay? Any tips for studying?</p>
<p>Or can anyone think of any little reminders/tricky stuff? For example… instead of Lagrange error, error is less than the next term of an alternating series going to 0? Or how to find the derivative of an inverse which everyone totally forgets… which is f’(x)=1/(f’[f^(-1)(x)])?</p>
<p>My teacher told our class that a problem involving finding the area bounded by the axes and a polar curve or indeed finding the area bounded by two polar curves would be likely this year because they haven’t shown up too much in the past few years.</p>
<p>Anyway, could anyone help me with Lagrange remainders? My study guide says that the error bound of an n-th degree Taylor approximation can by given by the value of the next-degree term once the value for x is plugged in. Is there anything else I need to know in addition to this?</p>
<p>There’s another lagrange remainder formula for when you’re calculating for a non-alternating series, but that’s got me confused too! I hope someone can clarify.</p>
<p>Also, for an equation of a polar curve, how do you find the limits of integration when finding the area?</p>
<p>If the question involves two polar curves, I usually set the two equations equal to each other and solve for theta. Otherwise, if the axes form part of the boundary, then I define the polar equation(s) parametrically and then find the value of theta that gives me the x- or y-value I happen to be looking for.</p>
<p>Hope that makes sense.</p>
<p>What do you do with just one value of theta though? For the limits of integration, there must be two values.</p>
<p>Like for example, when finding the area of the polar curve r=1+2cos(theta), how are the limits of integration 2pi/3 to 4pi/3?</p>
<p>@Ronaldofan94 that’s for an alternating series going to zero. Lagrange= [f^(n+1)(c) (x-a)^(n+1)]/(n+1)! Usually the f(c) thing is something that it has to be less than…it’s kind of hard to explain and it depends on the problem.</p>
<p>@dchau503 Okay so for that polar curve, I’m guessing youre trying to find the limits for the area of the loop inside of it. So the loop starts/ends at the origin which is where r=0. So you have 0=1+2cos(theta), or (-1/2)=cos(theta). So theta=2pi/3 and 4pi/3</p>
<p>Omg ty so much Morgan, that makes so much sense now. </p>
<p>Also, for 5b,</p>
<p><a href=“College Board - SAT, AP, College Search and Admission Tools”>College Board - SAT, AP, College Search and Admission Tools;
<p>how did the key get the solutions for the answer? I tried plugging (0, root(2)) into the derived equation and it didn’t get 1/2.</p>
<p>Are the shell/disk/washer methods on the test? My teacher barely went in depth with that. 0_0</p>
<p>So if you solved 5a right you have dy/dx. You want every point (x,y) where the slope is 1/2 or where dy/dx = 1/2. So setting dy/dx = 1/2, we have y/(2y-x)= 1/2 -> 2y=2y -x, subtract 2y from both sides, 0= -x or x=0. So dy/dx = 1/2 where x= 0 . To find the y coordinate, we plug x=0 into the original equation, y^2=2+xy -> y^2 = 2 + (0)y -> y^2 = 2 -> y= 2^(1/2), y = -(2^(1/2)). So the desired points are (0, 2^(1/2)), (0,-(2^(1/2)))</p>
<p>Yea you plug in x=0 back into the original equation not the derived equation.</p>
<p>@SHINeeTiara My suggestion is to go to youtube and type in “volumes of revolution” shells or washers and watch PatrickJMT’s videos. He explains them really well IMO as well as a ton of other calc things. My teacher was crazy this year so whenever I didn’t understand something I went to youtube :)</p>
<p>Spent 8 hours on calculus today… I think I have a chance at getting a 5 now! Whoot. I’ve been doing really well on class-offered mock AB exams (90+), so hopefully I won’t bomb BC too much. Planning on taking a mock BC tomorrow.</p>
<p>Thank you Morgan. Also, do we do the free response in pen or pencil?</p>
<p>@SHINeeTiara:</p>
<p>I took AB last year, and we did free response in pencil. So I would assume the same applies for this year.</p>
<p>Also, if anyone is looking for last minute multiple choice practice, here is the compilation of all released mc from 1969 up until the late 90s.</p>
<p><a href=“http://staff.4j.lane.edu/~windom/AP/ap%20multiple%20choice.pdf[/url]”>http://staff.4j.lane.edu/~windom/AP/ap%20multiple%20choice.pdf</a></p>
<p>Also, the most recent released AP Calc BC Multiple Choice (2008):</p>
<p><a href=“School Website, CMS & Communications Platform | Finalsite”>School Website, CMS & Communications Platform | Finalsite;
<p>My calculus teacher is awesome and we had a review party today at someone’s house with food and everything. I’m so ready for this test. I just have a short checklist of things to review on my own and two or three derivative formulas that I don’t remember (but haven’t seen for months/on the four full practice APs I’ve taken). YAY CALCULUS.</p>
<p>Any resources for sketching slope fields or recognizing them from graphs?</p>
<p>For help with Taylor/Maclaurin series, a friend of mine showed me this. Explains it a lot better than my teacher did: [Maclauren</a> and Taylor Series Intuition - YouTube](<a href=“Taylor & Maclaurin polynomials intro (part 1) | Series | AP Calculus BC | Khan Academy - YouTube”>Taylor & Maclaurin polynomials intro (part 1) | Series | AP Calculus BC | Khan Academy - YouTube) He has others that help a lot also. I’d check it out. Little long, but worth it</p>
<p>Not ready for BC at all >_<</p>
<p>SHINeeTiara: For sketching them, I honestly just plug stuff in and draw. They suck. I don’t know if there is any other way. For identifying the differential from the graph, I usually look at the differential and think: does this depend on only x? (only x is there) in that case, it must be one that is different for different x vales. if it depends only on y, then it will be the same thing all the way across and only change as you go up and down. if it depends on both, then they’ll be different both directions. neither and it will be the same everywhere. Then you can just plug easy numbers in and try to find the right one from there. It’s an inexact science.</p>
<p>If the differential equation is a function of both x and y, then I just make a table that gives me the value of the derivative with a particular combination of x and y. Recognizing them from graphs can be a bit tricky, but it shouldn’t be too bad if you make a table. If you’re asked to find a general (particular) solution from the slope field, then just use the tangent lines indicated by the slope field to sketch a general solution and see which of the answer choices best fits the graph you sketched.</p>
<p>Hope this helps.</p>