***OFFICIAL AP Calculus BC Thread 2013***

[elf4EVA]

Turns out, my school won't let me take BC Calc (I'm taking Honors Precalc instead, even though I've already studied precalc). So I'll likely self-study calc during the year using my school's textbook, Barron's, AMSCO, Khan Academy, Patrick JMT, OCW, and anything else I might find useful.

[elf4EVA]

Oh yeah, I forgot to include PR as well.

[elf4EVA]

What are you guys doing in your BC Calc class right now? I'm self-studying, and as of now, I've pretty much learned all the basic methods of finding limits and derivatives (power rule, product rule, quotient rule, chain rule, implicit differentiation), as well as some L'Hopital's rule.

[CantConcentrate]

Our class is learning about the Second Derivative Test and concavity right now. I've already taken Calc I though, so it's mostly review.

[Mansu007]

Are Khan Academy and Patrick JMT good resources? Do they explain the concepts and principles in understandable way?

Also I have a question.

what is the derivative of (cosX)^X ?

What is the derivative of (-arccos (1/(X^4)) ?

[Flamewire]

@Mansu007:

d/dx (cosx)^x - use the chain rule

Let cosx = z (this is a way to make sense of the chain rule if you don't yet have the intuition; substitute the inside function for another variable and differentiate with respect to it)

If y = (cosx)^x, then the derivative of y (dy/dx) equals dy/dz * dz/dx

dy/dz = d/dz z^x = ln(z)*z^x
dz/dx = d/dx cosx = -sinx

dy/dx = dy/dz * dz/dx = ln(z)*z^x*-sin(x).

Now, we want the final answer in terms of x, so substitute cosx back in for z.

dy/dx = -ln(cos(x))*(cos(x))^x*sin(x)

For the second one, -arccos(1/(x^4)) = -arccos(x^-4).

Use the same strategy as above, but using the chain rule means that the derivative of that function derivative of the inside times the derivative of the outside taken at the inside.

derivative of inside (x^-4) = -4x^-5 (this is the power rule)
derivative of outside taken at the inside (-arccos(z)) = -1 * -1/sqrt(1-z^2) = 1/sqrt(1-(x^-4)^2) = 1/sqrt(1-x^-8)

Therefore, the derivative is -4x^-5 * 1/sqrt(1-x^-8) = -4x^-5/sqrt(1-x^-8)

[dotdotdot77]

I'm sure everyone has heard the same question by now, but i feel the need to ask this. PR or Barrons? or is there another review book out there that's better? i know it's really early to be thinking about the AP test and review books, but i made the most amazing and wisest decision ever to take 5 Ap classes this year so i want to jump ahead.

i'm so looking forward to the written section on the test. *sarcasm* i look forward to dying this year and anyone and everyone is welcome to attend my funeral!

[Darthpwner]

For the people who are NOT self-studying the class, wouldn't the teacher be sufficient? My teacher gives a lot of practice AP material so I don't really need a review book.

[tangentline]

^Teacher + Hw is sufficient

Last year was AB, this year is BC and we're going at a rate that can be faster because the first 2.5 weeks was AB review and we take warmup time and every Friday off to do AP test practice (The teacher has never ever had a failing AP tester!)... Currently at Trigonometric Substitution and Partial Fractions. However by the quarter/block system everything BC except for infinite series is going to be done by this quarter which ends early October.

It's a breath of fresh air with all of the other AP classes in the way, and the tests have problems that weren't specifically taught or in the homework, and is great practice for Calculus competitions as every now and then I catch a mistake not to make again, revisit problems, and explore new ones

[mathrom]

Could anyone explain to me delta-epsilon proofs? I understand how to solve the problems, but I'm nearly clueless about what I'm doing.

[CantConcentrate]

Eww, you don't need to know what those are for the exam, but...

Let's say we want to prove that the limit as x approaches 3 of 4x-1=11.

We can say:
Given Epsilon > 0, let delta = E/4. Assume 0<|x-3|<delta.
|f(x)-L|=|(4x-1)-11|=|4x-12|=4|x-3|
4|x-3|<4delta
4(E/4)=E

You have to use the identities |f(x)-L|<E and 0<|x-a|<delta

[byahnoob]

PRINCETON REVIEW is by far better than BARRONS.

barrons just gives you worthless difficult problems
while
princeton review gives you thorough examples
(for practice problems, find official ap calc MC and frqs)

[potatochipsdojo]

Barrons is like a mini-textbook for many subjects while PR actually helps you review. That said, if you get comfortable with the problems on Barrons, the AP exam should be a real breeze.

[Synapses]

Hello everyone. So here's my situation.
This summer, I decided to self - study Honors Algebra 2 and take a class for Honors Precalculus at the same time. I completed the class, which turned out to be not very complete in its teaching of the topics supposed to be covered. The class did teach Trig and vectors pretty fully but not polar or parametric in as much detail. For the topics that i felt were not fully covered in class, I learned from Khan Academy and other internet resources.
When I tried to test out in school, the math coordinator said I passed Algebra 2 but not Precalculus. However, he didn't seem very happy about me testing out and I have heard from other students that he is not completely reliable or truthful; but it doesn't make a difference now.
The main question i'm asking now is: Do you guys feel that I can self-study Calculus BC by the AP Exam? Also, what textbooks should I be using for this purpose?

[dirkslam41]

guys If u search google, there's a compiled list of all the multiple choice since 1987 I think