<p>hey mikeandthemaddog,</p>
<p>"
sin(x) = x - x^3 + x^5 ... (-1)^n * x^(2n+1)
cos (x) = 1 - x^2 + x^4 ... (-1)^n * x^(2n)
e^x = 1 + x + x^2 ... x^n
"</p>
<p>all of those are WRONG</p>
<p>sin(x) = (-1)^n * x^(2n+1) / (2n+1)!
cos(x) = (-1)^n * x^(2n) / (2n)!
e^x = x^n / n!</p>
<p>you should also know arctan:
arctan(x) = (-1)^n * x^(2n+1) / (2n+1)</p>
<p>note that the only difference between sin and arctan is that arctan does NOT have the factorial in the denominator.</p>
<p>Oh, i didnt even realize that all of them were wrong! Oops, Mike, you HAVE to divide by n! That is the definition of a taylor series. MAKE SURE YOU KNOW THE DEFINITION!!!! </p>
<p>Also, I have a question. Do we need to know the Cauchy Product Theorem for multiplying series??? I learned that, but have not seen it in any review books.</p>
<p>thanks.</p>
<p>Wow. I'm guaranteed to score a 0.5. -_-"</p>
<p>My original Question:
[quote]
1) Partial fractions. I am looking at an example in my book, and it says you can write:
2/(4n^2-1) = 2/(2n-1)(2n+1) = (1/(2n-1))-(1/(2n+1))
How does that second part = the third part?
[/quote]
</p>
<p>Your answer:
[quote]
1. Patrickk's Q on Partial Fraction
First of all, the book is right because if you expand the third part, you get the second part. Now how? This is pretty simple if you know how to do Partial Fractions.</p>
<p>Let A be the number on top of 2n-1 and B be the number on top of 2n+1. Then:</p>
<p>A/(2n-1) + B/(2n+1) = A(2n+1) + B(2n-1) = n(2A+2B) + (A-B) = 2
we know n's coefficient is 0 so 2A+2B = 0 and A-B = 2 --> -A = B and -2B = 2 --> B = -1 and A = 1. That's how you get the third part.
[/quote]
</p>
<p>Thanks. I need to do somemore reading on partial fractions.</p>
<p>Is there a possiblity that we will have some "more" difficult partial fractions questions where you must add a third variable or make the variables (A/B) squared. I remember doing some of that, but its not covered in the barrons. </p>
<p>Any clarification would be nice. </p>
<p>Also, how do would you draw graphs that you plot on your calculator. I've read something about having to show your "window" or something like that. I have no clue what this means, and I've never learned how to use a calculator to that. Please explain, thanks</p>
<p>Oh yea almost forgot, I have a question about limits. Here's the question (from barrons p.573, q9):</p>
<p>lim h->0 [(25+h)^1/2-5]/h</p>
<p>A.=0 B.=1/10 C=1 D=10 E. Does not exist</p>
<p>I thought the answer would be C but barrons says it should be B. Anyone care to explain.</p>
<p>P.S. is it just in the barrons book that "does not exist" is almost NEVER a correct answer or are CB test like that too?</p>
<p>Edit: one more thing, how do you estimate an integral? Also, a tip to people who don't know this, if you have a trig function in a limit question, replace it with the first term of its taylor series: Ex: sinx/x=>x/x or cosx/x=1/x.</p>
<p>For the partial fractions:
[ol]
[li]f(x)/[g^2(x)] = A/g(x) + B/[g^2(x)]
[li]f(x)/[g(x)h(x)] = (Ax + B)/g(x) + C/(h(x)
[/ol]
*where g(x) in the second equation is a non-reducible quadratic</p>
<p>I think that you just have to indicate what your units are (i.e. does each little notch on the axes signify 1 unit or 5. units). You can set this (and your window) by hitting the window button (yellow, f2) on the ti-89.</p>
<p>The limit is the derivative of sqrt(x) at x=25. dy/dx sqrt(x) = 1/[2sqrt(x)]. Plug in 25 for x to get 1/(2*5) = 1/10.</p>
<p>To estimate an integral, use Riemann sums (left, right, trapezoid, etc.)</p>
<p>Atomicbomb22: What they are doing there is finding the derivative of f(x)=x^0.5 @ x = 25 using the definition of a derivative. (i.e. lim h --> 0 [f(x+h) - f(x)] / h)
f(x) = x^0.5
f'(x) = 0.5x^-0.5
f'(25) = 0.5 / 5 = 1/10</p>
<p>Just an addition to previous poster's answer on limit, anytime you see question like this:</p>
<p>lim h--> 0 (f(x+h) - f(x))/h = d/dx (f(x))</p>
<p>This appears A LOT so make sure you learn this.</p>
<p>I have yet to see partial fraction question involving three on practice exam. If you're unsure, test some numbers with choices to see which one's right :-P. heck, if you can brute force question in Calculus exam, do it. You don't need to do all calculus question to solve them and test graders won't ask, "did you use calculus for each one?"</p>
<p>Yeah, I'm with grayfalcon89.</p>
<p>Watch out for things like using different integrals for volumes of solids of revolution (i.e. in terms of y as a disc and inters of x as a shell). PRs book had some of these, and it's time consuming to have to evaluate all of the answer choices. I don't know if the AP test has them too.</p>
<p>Barron's said that there are no shell questions on the AP exam.</p>
<p>Yeah my teacher says that there are revolution questions that you only need to know disk/washer for, but that shell could be helpful.</p>
<p>I hope there are no questions regarding cylinders or cones.
I can never remember the formulae for those.</p>
<p>i second that... the whole volume thing seems like forever ago... </p>
<p>the only things i have on lock are integration by parts and l'hopital's rule...haha... can i get a 1 on BC but a 4/5 AB?</p>
<p>Here is an excellent site that can help you: <a href="http://tutorial.math.lamar.edu/AllBrowsers/2414/2414.asp%5B/url%5D">http://tutorial.math.lamar.edu/AllBrowsers/2414/2414.asp</a></p>
<p>It covers everything from cross-sections, sequences + series, and more. For AB topics, click on Calculus I under Class Notes at the top.</p>
<p>I just read this on Wikipedia:
AP Calculus BC is also the highest scoring AP Exam out of all the other Advanced Placement Exams.
The approximate curves for a 5 are 75% for the AB test and 65% for the BC test.</p>
<hr>
<p>Also, what programs do you all have on your calculator to help you? I don't have any additional ones really. I will be using Solver, fnInt, and nDeriv, but anything else we need extra? Thanks</p>
<p>PatrickK: I know about fnInt and nDeriv, but could you tell me about what Solver is and how helpful it is? Thanks.</p>
<p>wow patrick. 65% for the BC? THat means that it is very hard to get points...</p>
<p>What is fnInt?</p>
<p>I wrote one for euler's method (cause I hate doing that crap - unfortunately, I think that most of the euler's method questions occur on sections for which you cant' use your calculator.) Hm... do you think it would be worth writing one for solids of revolution?</p>
<p>Solver just solves equations for you. For example, type x^2 + 3x - 15 = 0 and forget about it. (It's f2, 1 on the ti-89. Unless anyone knows something about it that I don't the solver on the 83s and 84s sucks because you have to give a range and it only finds one solution for you. For anyone who's using an 83 or 84, I'd just graph it and find the zeros that way.)</p>
<p>For Euler's method, just use a table.</p>
<p>I copied down a trapezoid rule one off of some website.</p>