<p>Okay: Logistic growth problem!</p>
<p>dP/dt = (P/5)(1-P/12)</p>
<p>If p(0) = 3, what is the limit of P(t) as t goes to infinity?</p>
<p>If p(0) = 20, what is the limit of P(t) as t goes to infinity?</p>
<p>12 for both.</p>
<p>sin(x) = summation n=0 -> infinity (-1)^n * ((x-a)^(2n+1)/(2n+1)!)
cos(x) = summation n=0 -> infinity (-1)^n * ((x-a)^(2n)/(2n)!)
e^x = summation n=0 -> infinity (x-a)^n/n!
arctan(x) = summation n=0 -> infinity (-1)^n * (x^(2n+1)* (2n)!/(4^n<em>(n!)^2</em>(2n+1)))</p>
<p>goodusername can you please explain how to came to that answer please! :)</p>
<p>M = 12 the carrying capacity, which mean it can hold only 12 :p hope this helps</p>
<p>if it asks when the population is growing fastest it is at 1/2(12) = 6 right? does that have to do with the number out front (P/5) in this case. If the number out front was say, 0.6, would the population be growing fastest at 0.6(12)? I'm self studying bc >.< lol</p>
<p>what is the formula for differential?
f(x+delta x) = f(x) + f'(x)(delta x)
is that right?</p>
<p>what does it mean when we are asked to write a derivative's in partial FUNCTIONS (not fractions). </p>
<p>For example i read this and didn't get it:</p>
<p>Find where the tangent line to f(x) is horizontal</p>
<p>It says: Write f(x) as a fraction. Set the numerator equal to zero.</p>
<p>Anybody???</p>
<p>Also good review sheet: <a href="http://yhspatriot.yorktown.arlington.k12.va.us/%7Ecpeacock/AP%20Calc%20Answers.doc%5B/url%5D">http://yhspatriot.yorktown.arlington.k12.va.us/~cpeacock/AP%20Calc%20Answers.doc</a></p>
<p>^ just put your equation in point slope and solve from there. y-y1 = f'(x)(x-x1) then rearrange. It's easier than memorizing some form. btw this was to austin</p>
<p>^^austin I think thats right. I remember that buy saying it looks like a straight line equation (thats what it really is) of the form:</p>
<p>Y=MX+C
Rewriting in this form gives:</p>
<p>F(x)≈f'(x)(x-a)+f(x)</p>
<p>hope that made sense.</p>
<p>Thank's Atomicbomb22.
I get it.</p>
<p>Oh I have a question. On Polar equation how do you determine the limit or boundary of the region if you are asked to find area or arc length? I always get stuck on it. Do you set the equation for 0 and then solve for x or something?</p>
<p>I think you can just use the calculator to trace the curve to find your interval. Or they give you the interval in most cases.
I have that concern too.</p>
<p>How important is the logistics curve?
It's not covered in PR. Nor did my teacher cover it.</p>
<p>Hey guys,
Could you please look at the BC FR for 2003 at problem 4 (a)?
Why do they have -3 less than x less than -2?
why not less than or equal to?
Is it because the graph starts at 3 and at x=-2, the slope of the graph is 0?
Here's the link to the question:
<a href="http://apcentral.collegeboard.com/apc/public/repository/ap03_frq_calculus_bc_23064.pdf%5B/url%5D">http://apcentral.collegeboard.com/apc/public/repository/ap03_frq_calculus_bc_23064.pdf</a></p>
<p>Find the Cartesian equation of the curve represented by x = sec^2(t) - 1 and y = tan t, -pi/2 < t < pi/2.</p>
<p>yeah austin don't include endpoints in max/min and concavity problems. i dont think they take points off if you do, but just don't do it.</p>
<p>do u think its possible to get a 5 even if you don't know all the material (i.e missing topics such as logistics)</p>
<p>Also is it just me or does it take aggesss for a polar curve to be graphed on the ti-89?</p>
<p>u dont have to know a lot of topics to get a 5. but the ones u know u better get those questions right if youre gonna omit the ones u dont know</p>
<p>HEY GUYS, DO WE HAVE TO MEMORIZE THOSE CSC, SEC, COT, CSC^2, SEC^2...ETC FOR THE INTEGRATION AND DIFFERENTIATION FORMULAS? I'm sooo nervous.</p>