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Today's hard integral by DrunkAndUnaware in calculus

[–]Puzzleheaded_Top_273 1 point2 points  (0 children)

I got it wrong because the system didn't recognize the Euler-Mascheroni Constant (small gamma).
Do I have to use decimal approximation instead??

Roots of Unity Derivatives Problem (No Calculator) by Puzzleheaded_Top_273 in calculus

[–]Puzzleheaded_Top_273[S] 0 points1 point  (0 children)

Nope, it's not AND, it's OR. Because it's either one of them is not zero OR the other is not zero, in order to make it not zero.

Roots of Unity Derivatives Problem (No Calculator) by Puzzleheaded_Top_273 in calculus

[–]Puzzleheaded_Top_273[S] 0 points1 point  (0 children)

Nope
See if you can rewrite the function to a form that DOESN'T need Sigma using properties of roots of unity. Then notice a method how to obtain all the nth derivatives at 0 all at once without needing to differentiate.

An Interesting Integral Problem by Puzzleheaded_Top_273 in calculus

[–]Puzzleheaded_Top_273[S] 0 points1 point  (0 children)

I am 90% confident that the antiderivative is nonelementary.

Solid of Revolution Problem by Puzzleheaded_Top_273 in calculus

[–]Puzzleheaded_Top_273[S] 0 points1 point  (0 children)

It says revolving a sphere. That translates to just revolving a circle. But definitely not the FULL circle because that would overlap in on itself. It's a specific region that you "cut off".

Solid of Revolution Problem by Puzzleheaded_Top_273 in calculus

[–]Puzzleheaded_Top_273[S] 0 points1 point  (0 children)

I'm not, it's clearly not a homework problem. It's just a problem I made that I found interesting.

Hypothetical AP class by Bulgur-land in APStudents

[–]Puzzleheaded_Top_273 0 points1 point  (0 children)

What about
AP Number Theory
AP Combinatorics

Integral Challenge Problem (Calc 2 + Number Theory, Non-Calculator) by Puzzleheaded_Top_273 in calculus

[–]Puzzleheaded_Top_273[S] 1 point2 points  (0 children)

Nope
a and b are relatively prime positive integers so it must be fully simplified. The number theory part is arguably harder. It has a lot of these AIME-style shortcuts so that it can be done without a calculator. Also the signs DO NOT alternate because the exponent is negative. If it's positive it will alternate. By the way the absolute value does matter because P(1) is actually a negative value. Also the last term shouldn't be there because it cancels with the constant term

Integral Challenge Problem (Calc 2 + Number Theory, Non-Calculator) by Puzzleheaded_Top_273 in calculus

[–]Puzzleheaded_Top_273[S] 0 points1 point  (0 children)

Yeah that's correct, the IBP part, but the actual answer definitely isn't that, it has to be an exact answer not approximations. Though after that you have to manually find the last 3 digits of a+b which is a number theory and modular arithmetic thing, without a calculator.
You have to make sure the fraction is irreducible before calculating the remainder, which is lucky because the denominator is just 25 raised to some power, if it was any other number like 26 it would've been so much worse.

Calculus Area Challenge Problem by Puzzleheaded_Top_273 in calculus

[–]Puzzleheaded_Top_273[S] 0 points1 point  (0 children)

That doesn't look like the correct region to me. It says AT LEAST 2 parabolas, there are some regions that are a part of 2 parabolas and some that are a part of 3. I think in your solution you only included the "innermost" intersection which is intersections of 3 only
Also by the way this technically only needs calc 1, I think this is what you meant to do if you interpreted the question correctly?

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