***Official AP Calculus BC Thread 2014-2015***

Test Preparation AP Mathematics & Computer Science
581

What did you guys do for the Taylor problem?

What I did:
a.) Ratio test and got that R is 1/3
b.) Took derivative of f(x) to get 1 - 3x + 9x^2 - 27x^3
Since it’s a geometric series, r = -3x. To get the rational function for f’(x), you use sum formula a/1-r. So: 1/(3x +1)
c.) I took the integral of 1/(3x + 1) (also finding that the + C is 0) and multiplied by the number of terms from the e^x series that the problem asked for. Wasn’t sure if this is the way to do it, but I feel it makes sense.

582

You are correct.

583

What did you guys get for d^2(y)/dx^2 of y^3 + y=x? I got -3/2 but I think that is wrong.

584

@aar2697 - I don’t fully remember my answers, but I know I got the same thing for you for a. Part b and c look familiar- I think I got the same thing as you for that also.

@vakiii - I don’t remember that problem coming up in the free response. However, I tried the question and came up with -6y/(3y^2+1)^3.

585

@aar2697 so I did 3/(1+x) instead of 1/(1+3x) cuz I was on a time crunch and I wasn’t thinking… What’s the score distribution for that problem?

586

Now I’m pretty sure I did number 6 wrong. I got 1/3 but, For part b, when asked to express f’ prime of a rational function for |x| < R, I just derived the general term for f to get the general term for f prime. And for part c, I just took the terms for e^x and the terms they gave you for f at the beginning of the problem, and multiplied them together, I probably only got a 3 for this problem…

587

@Oblivion96 what were you supposed to do for the g(x) in the last problem then? I did what you did and got x-(3/2)x^3

588

@talocruz That’s what I got.

589

@taiocruz So when it said rational function for f prime for |x|<R, it wasn’t deriving the general term for f, it was plugging in -3x into a/1-r?

590

@oblivion96 the question asked to fin g(x) which = e^x(f(x)) or something like that

591

@oblivion96 When you write out the Talyor Series of f’, you recognize it is a geometric series and therefore you can write it in the form of 1/(1-r) (in other word, a rational function or a quotient)

592

I just realized in 6© I’ve stupidly multiplied e^x with f’ while the question is actually asking for just f
How many points will they take off for that?

593

If I didn’t write out the correct rational function, but I did everything else right, I probably still got a 6 or 7 right?

594

For the partial fraction, did you get like two terms involving 1/6*ln abs (###) +C?

Also for the m=/b= question, I think CB should have switched parts c and d to make the intended question more apparent.

595

Yep @agupte

596

I forgot to add c, though

597

Do you have to simplify it? My teacher did not require that we combine the logs into one big log.

598

@rdeng2614 - I didn’t simplify it; as they didn’t ask for it as one log, I doubt they would expect it simplified that way unless they asked for it.

599

What did you guys get for the logistic MC question? I got .00035P(p-500) but I’m not sure if that’s right or not.

600

@taiocruz I’m pretty sure you guys are both wrong. Several friends and I all got x - x^2/2 + 2 x^3. I just plugged this into mathematica as well and got the same answer. You just have to multiply the first 3 terms of the series of e^x with the series of f(x) that they give you.