<p>Series are like 1/6 of exam, and you only need like 60-65% for a 5, giving you about 20% room for error on the stuff you know, if that makes sense.</p>
<p>There almost always is a FRQ about a Taylor/Maclaurin series, and it usually asks for the interval of convergence. So, you’ll need Ratio test and 2 others, depending on the interval you get with ratio.</p>
<p>Can anybody give a brief summary about the formulas we need for logistic growth and carrying capacity?</p>
<p>Formula is</p>
<p>f(t) = A/(1+ce^(-Akt)) isnt it?
Where A is lim (t–>+infinity) f(t).
Just a quick question cuz I forgot,
Is carrying capacity “A” on the above formula?</p>
<p>Initially the amount is A/(1+c) at t=0 and the rate or df/dt is maximum when t corresponds to A/2.</p>
<p>Speed is a scalar, it has to be positive.</p>
<p>lemone// oops. if you are referring to some old post, then i might be wrong but
we are currently talking about logistic rate/growth and such.</p>
<p>Oh wait to answer your question, yes A is the carrying capacity. That is what it says in Peterson’s at least.</p>
<p>just a hint… AP Physics, at least AP Phys B, makes motion way easier to understand. I just had to skim it through.</p>
<p>yeah, knowing some physics helps with some calc. for example on frq 2009 form b, question # 2 talks about a function f(t) being the rate. then you know f’(t) is the acceleration and integrating f should give you position. . . with this knowledge the rest of the problem becomes easier. </p>
<p>2 more days guys good luck.</p>
<p>It’s also important knowing the logistic differential equations:</p>
<p>dP/dt = kP(1 - P/L),</p>
<p>Where P is population, k is any constant, and L is the lim(t->infintiy) P(t). The “1” is very important. Say they ask you the carrying capacity of a population and gave you</p>
<p>dP/dt = 5P(2 - P/100)</p>
<p>You have to factor out a two, then you’ll be able to clearly see your L.</p>
<p>2 more days and then the Calc is over with. Then I got the ridiculously hard Lit. Ugh. My prediction is 5 and 1 respectively.</p>
<p>Finally, exam is in 2 days…</p>
<p>Good luck, everyone</p>
<p>Im just trying to remember all those tests for series and whatnot. And memorizn the basic taylor series</p>
<p>…So I should probably start studying, eh?</p>
<br>
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<p><a href=“College Board - SAT, AP, College Search and Admission Tools”>College Board - SAT, AP, College Search and Admission Tools;
<p>question 6b, where did they get 1/2 from?</p>
<p>These are questions I have from a review book that I’m having trouble with. If anyone could help me out I’d appreciate it! :)</p>
<p>1) The region in the first quad. enclosed by the graphs of y=x and y=2sinx is revolved around the x-axis. The volume of the solid generated is…</p>
<p>and the answer is 13.355</p>
<p>I keep getting 2.126 by doing pi*defint of ((2sinx)^2-(x)^2))dx from 0 to 1.895495. I found the numbers on my integrand by setting x=2sinx. What am I doing incorrectly?</p>
<p>2) Here’s another problem. The base of a solid is the region in the first quadrant bounded by the line x + 2y = 4 and the coordinate axes. What is the volume of the solid if every cross section perpendicular to the x-axis is a semicircle?</p>
<p>the answer is 2pi/3, but I keep getting 4pi/3.</p>
<p>I am doing pi/2* the def int of ((2-(x/2))^2) from 0 to 4. I made the equation into a y-equation for the integral.</p>
<p>I found a few more questions I have from the book. Hopefully someone has some crazy desire to help me out? It’s a good way to study…:)</p>
<p>anyway.</p>
<p>1) If n is a positive integer, then lim as n approaches infinity from the rt, of (1/n)(sin(pi/n) + sin(2pi/n) + … + sin (npi/n) is</p>
<p>the answer is 2/pi. I stink at these types of questions. So any type of explanation is especially appreciated.</p>
<p>*calc2) How many zeros does the function y=sin(lnx) have for 0<x<or equal to 1?
I graph it, and I get only 1. But the answer is more than 4… huh!?</p>
<p>*calc3) Let f(x)=x^3 - 7x^2 + 25x - 39 and let g be the inverse function of f. What is the value of g’(0)?
The answer is 1/10.</p>
<p>So I know to switch x and y to get the inverse, but I don’t know how to get to the derivative. If I switch x and y, I then get x=y^3 -7y^2 +25y.
If I differentiate this, I get dy/dx=3y^2 - 14y + 25. But I really have no idea where to go from here.</p>
<p>*calc4) final question! promise! A rectangle is to be inscribed in a semicircle of radius 8, with one side lying on the diameter of the circle. What is the maximum possible area of the rectangle?
The answer is 64.</p>
<p>I know I have to use the area formula and optimize it by setting the area =0, but I’m confused about what values belong where in the equation.</p>
<p>If anyone actually sat through and even read all my questions, thanks SO much!!!</p>
<p>
</p>
<p>Funny, I got 6.677 which is half of the answer (13.55/2 = 6.677…) I have no idea how you got 2.126.</p>
<p>I put this into my calculator</p>
<p>Y₂ = 2sinx
Y₁ = x</p>
<p>πfnInt(Y₂² -Y₁², X, 0, 1.895) = 6.677</p>
<p>
</p>
<p>For this one, I got what your book had</p>
<p>Y₁ = (2 - 0.5x)²</p>
<p>I typed this into my calculator</p>
<p>(π/8)fnInt(Y₁, X, 0, 4) = 2.094…</p>
<p>Which is the same as 2pi/3</p>
<p>why did you do pi/8?</p>
<p>Can anyone help me out with this? </p>
<p>The length of the path described by the parametric equations x=2sint and y=3cost for 0<t<pi/2 is given by?
**the < are really less than or equal to…</p>
<p>isn’t length just the integral of the square root of dx squared + dy squared?</p>
<p>my book is giving me a different answer… thanks.</p>