@Aphirox the series with f(x) was four terms and the e^x was three. to multiply them would require 12 terms and would be excessive
for area between polar curves, you can think of it more logically and you will remember it much better than if you try and remember a rule of thumb. So you can just think of it as: find the entire area, subtract the area you dont want and it gives area you are looking for, so its different every time you just have to think about when your taking the integral, what area does it give you. You can also think of it like this: Integral(f(x)-g(x)) = Integral(f(x))-Integral(g(x)) so you can separate them and determine what area they give individually, so then you can decide which to subtract from which, or which area you don’t want and subtract that integral from the entire area. Its the same as cartesian curves because they both generate similar areas, you just have to keep in mind HOW the areas are generated. For cartesian, from a to b on the x-axis. For polar, it creates triangular sectors up to the curve, starting at the origin and immediately radiating to angle alpha and scans along the theta axis to beta, creating triangles.
@noname054
it asked for a rational function, and now I see how what you said is right, a/(1-r), but do you think we would get credit for writing the general term, which also happened to be rational?
@Aphirox - I don’t 100% remember but think that’s what I got for part 6c.
@Aphirox e^x = 1 + x +(x^2)/2…
f(x) = x-(3/2)x^2…
g(x) = f(x)(e^x) = (1x) + (x (-3/2)x^2) = x - (3/2) x^3
Did i mess up somewhere?
@taiocruz You didn’t foil correctly. Check all you terms.
@Newdle I didn’t foil. i just multiplied term by term.
@taiocruz - I think you should foil- that’s what I did. I foiled out (1+x)*(x-3/2x^2).
@taiocruz Yeah, you missed a few terms. For example, you should have an (x^3)/2 term in there somewhere.
I multiplied it out like taiocruz did and foiled it to see if I got the same answer. I did. I got x-1/2x^2-3/2x^3. Is this right?
@Mathinduction ahh i see where i went wrong now
For the rational function part, I don’t think they will give full credit for just the general term, because you can’t really say a series (even with a quotient behind the sigma) is a rational function
Am I allowed to post a link to some tentative answers? I saw online where someone did the problems and they seem to confer with popular consensus.
@rdeng2614 Please do!
@Aphirox I got that too… I don’t see what the issue is
MODERATOR’S NOTE:
It depends on the link.
Here are the links. @skieurope You can remove them if you think they violate any sort of terms/conditions, just don’t ban me please. Thanks
BC:
http://www.calculusquestions.org/docs/apcalculus/apexams/cbfreeresponse/2015_bc_form_a_solutions-shubleka.pdf
Anywhere the answers are wrong, please someone point them out.
These aren’t mine btw.
@rdeng2614 The links are fine. Thanks for posting.
Askmrcalculus (google that) also has the answers posted. They’re the same, so I’m assuming those are the correct ones and people can accurately predict their free response grade based off of that.
For 6c. shouldn’t the x^3 term be 3 (from 1x^3) - 3/2 (from xx^2) + 1/2 (x^2*x) = 2. The stuff in parentheses means which term I took from e^x and multiplied from the other term from the f(x) expansion.