@Frigidcold What is process flow?
@agupte @Kazoo98
He means for series. I’d say there’s probably about 50% for there to be a remainder problem. But, 2/3 of the remainder questions actually involve the alternating series error as opposed to the Lagrange error. Neither is very difficult. I can explain if you like.
@rdent2614 Mostly conceptual stuff. Some pretty basic differentiation/integration.
I’m pretty sure you can still calculate the lagrange error bound without using a calculator by changing the M to an “easy” number" - correct me if I’m wrong though.
@blargenshmargen Correct, generally you can round to a very easy “maximum” value. You generally don’t even calculate the error, just prove it’s less than a certain value.
@Frigidcold Isn’t Lagrange error where you evaluate the next term for a point (z) where it makes the expected error the the most?
@rdeng2614 There are generally a few simple differentiation/integration questions on the non-calc MC. There are a number of charts and graphs for things like Riemann Sums, Fundamental Theorem questions, and conceptual first/second derivative stuff. Usually there are at least 3 MacLaurin/infinite series kind of questions, you’ll almost definitely see one that has 3 series and asks which of the 3 converge or diverge. Other somewhat common topics: parametrics, logistic differentials, and L’Hopital’s rule.
@EveningSwan There may be another name for it, but my teacher calls it process flow. Basically ones that give the rate function and you find stuff with it. Examples include 2014 #1 and and 2013 #1.
@Kazoo98 Yep, general gist of it. Pretty similar to the alternating series error, which like I said, is more common than Lagrange.
@IntegralOfPi Could you explain the convergence and divergence tests in a simple manner? I know geometric series and P series, but otherwise, I know there’s an integral test, but I don’t know the specific conditions where the test could or couldn’t work.
MODERATOR’S NOTE:
As long as the links don’t get posted here, and nobody asks for the links here, be my guest. Of course, someone invariably destroys it after about 5 minutes.
@Kazoo98 http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/SandS/SeriesTests/test_summary.html
I’d imagine your textbook has some sort of chart, at least mine does. Ratio test is the most common, almost guranteed to be on the test.
Is it likely that there will be an FRQ question where it asks whether a series converges conditionally or absolutely?
@blargenshmargen Unlikely to my knowledge. That would be a multiple choice question. I’ve seen FRQ’s say that this series is alternating and convergent, then it asks about the error.
I am very confused about euler’s method can somebody explain how to do it?
@Kazoo98 This may help you: http://i.im gur.com/7AuEgGU.jpg
(btw the telescoping series is not on the AP exam)
@kolaman17 Euler’s method can be done in any amount of steps. The more steps, the more accurate the prediction is. In order to determine f(1.5), you would need a value for f(1) and f’(1). The function would be f(1.5) = f(1) + f’(1)x. Where x is the change in x. If you wanted to approximate f(2), you would use the previous prediction. f’(1.5) would be stated somewhere or could be easily found.
In short, we are adding the derivative at a point times the change in x in order to calculate the displacement of the particle. We then add that to the original value.
Can someone explain the error for series? My teacher never talked about it.
I’m just practicing with an frq of some random year and my ap prep book. It’s important to sleep early, as I’ve learned from today :).
@JuicyMango How’d you do on chem?