It depends on what difficulty problems you'd like. But, I can give you some math problems that should hopefully not be too bad. If you'd like some that are easier or harder, you can ask, but here are a few to start.
1. Explain why the derivative of f(x) = x is 1.
2. Simplify* the expression (x + 5)(x - 5).
3. Given that an integration operation reverses the derivative, why must we add "+ C" at the end of our solutions to indefinite integrals?
#45 would be right if I set the expression equal to zero, but I was asking for it factored, not solved. The expression might not equal zero at all, as I never specified. So, #43 was correct in response to the second problem I posted.
Yeah, you're right, my bad, lol. Thanks for calling me out on that! I'll edit that right now.
Problem 4: Explain why i^4 = 1.
(Note: i is not a variable, rather it is a complex number with imaginary part i and no real part.)
The factorial operation n! multiplies every number from n down to 1. This means that in order to get from (n - 1)! to n!, you just need to multiply by n, since that would be equivalent to just straight-up taking the factorial.
For example, 4! = 4 * 3 * 2 * 1 = 24. 3! = 3 * 2 * 1 = 6. Set k = 3!, so k = (3 * 2 * 1). Thus, since 4! = 4 * 3 * 2 * 1, we see that we can replace the last part with k, such that 4! = 4k. We can easily expand this to fit any factorial where n is a natural number.
Explain the reasoning behind Stirling’s approximation without looking it up.
make children cry.