edited to remove the same gazillion places of pi3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058
By preferred order:
1 Apple...don't care about the ice cream (but wouldn't pass if it came with it)By preferred order:
1. Lemon Meringue
2. Blueberry
3. Cherry
4. Apple
5. Strawberry Rhubarb(?)
6. Pumpkin
I don't even know what rhubarb is. Pumpkin I can only do over Thanksgiving, and apple HAS to have vanilla ice cream.
Why? Is it something you eat regularly? I can't remember when the last time was I had apple pie. We bought a frozen one from our nephew as some kind of fundraiser he was doing a few years ago and that thing is still sitting in our freezer lol. Oh, pretty sure it doesn't count, but I got a couple of apple pies from McD's a few months ago.I'm so over apple pie. Oy.
The details of showing f^{(j)}(0) and f^{(j)}(pi) are integers are a little tedious and depend on a binomial theorem like expansion for finding the nth derivative of a product of two functions but it's pretty straightforward. The most advanced result used in the proof is that c^n/n! goes to zero as n gets arbitrarily large for any constant c, but pretty sure that gets taught in calculus too, and not saved for real analysis.You must have gone to a different high school.