Recent content by Zhalfirin88

That's exactly what I put, 0, and it was marked wrong. I'm trying to figure out why it was marked wrong

Homework Statement A car is going down an incline with a constant acceleration. [b]How much work was done on the car by the force of the road going down the hill? (neglect energy losses due to air resistance, rolling friction, etc.) The Attempt at a Solution There are 2 forces acting on...

OK thanks. I didn't consider X to be a single element, then any nonempty subset of X would not be in {null, X}

Homework Statement Show that X is connected if and only if the only subsets of X that are both open and closed are the empty set and X. Proof: https://files.nyu.edu/eo1/public/Book-PDF/Appendix.pdf Page 14. I'm confused by this proof. First, if S is not in {null set, X} then how can S...

Yes, an analysis class, but yeah it's a little awkward, especially since the professor used a derivative to prove some lemma or something, then goes and says "we shouldn't be using derivatives yet, but I'll use it anyways" :) And no we have not defined e^x yet, correct

Actually, since a_kn^k/e^n \leq an^k/e^n is the largest term of the polynomial, couldn't you just find a N that suits this expression? Because p(n)/e^n can be written as \frac{a_0}{e^n} + \frac{a_1 n}{e^n} + ... + \frac{a_k n^k}{e^n} , and since you choose n > N always, then the N that you...

No we are proving things based on the definition of convergence, for instance, our proofs start off as "Let \epsilon > 0 be arbitrary, and choose N > ... such that for all n > N ... etc. We haven't done epsilon delta proofs yet.

I don't think I'm allowed to use L'Hospital's rule, we have not proven it in class yet.

Homework Statement Prove \lim_{n\rightarrow\infty} \frac{p(n)}{e^n} = 0 where p(x) = a_k x^k + ... + a_1 x + a_0 (with real coefficients a_i in \mathbb{R} ) The Attempt at a Solution I thought about using series to try and prove this, but I couldn't get it to work out and I think...

If you did this by modular arithmetic you would have to take by mod 2 and mod 3, correct? And the remainder is zero =)

Thanks :)

Kinda induction, but I'm guessing that's not what you're getting at? If f(a+1)−f(a)=6(a^2+2a−1) and we assume f(a) is divisible by 6 then f(a+1) is also divisible by 6.

6a^2+12a+6 Each term is divisible by 6, so it works, but I'm not really sure where you came up with subtracting expressions?

I have no idea what you're doing with that hint. I reduced it but I don't get why substituting (a+1) and subtracting the expression for a works? Okay, I reduced it to -2a^3+2a^2-a but . . I'm not sure what you mean by rewriting it?

Homework Statement Prove that, for any integer a, 6 divides a(a+1)(2a+1)The Attempt at a Solution Well, 6 divides something if 2 and 3 divide the same number, so I must show that that product is even, and that the sum of its digits is divisible by 3. However, I don't see any algebraic...