Recent content by tehdiddulator

Homework Statement In my book, for a class on numerical analysis, we are given the definition: "Suppose {β_{n}}from n=1 → ∞ is a sequence known to converge to zero, and \alpha_{n} converges to a number \alpha. If a positive constant K exists with |\alpha_{n} - \alpha|≤K|β_{n}|, for large...

Homework Statement x' = \begin{pmatrix}0&1&3\\2&-1&2\\-1&0&-2\end{pmatrix}*x The Attempt at a Solution I've found the repeated eigenvalues to be λ_{1,2,3}=-1 I've also found the first (and only non zero eigenvector) to be \begin{pmatrix}1&2&-1\end{pmatrix}, but I'm not entirely...

Everything worked out properly! Thanks a bunch for your help.

Ah, I suppose I should add in the major fact that they want it in terms of the generalized coordinate rho. I can try and find/make a picture of the graph if it helps. and yes, you are correct, the potential would be mgz.

Homework Statement Consider a bead of mass m sliding without friction on a wire that is bent in the shape of a parabola and is being spun with constant angular velocity ω about its vertical axis. Use cylindrical polar coordinates and let the equation of the parabola be ##z = kρ^{2}##. Write...

For the 3sin(x) would the guess of the particular solution be in the form of A*sin(x)+B*cos(x) and for the other term, would it be in the form of (C*x + D)*(Fe^{-x})?EDIT: Changed T to x

Homework Statement He tells us to find the form of the particular solution without having to compute the actual particular solution. For Example, (D^{2}+1)y = xe^{-x}+3sinx Homework Equations I'm not even 100% sure how to begin...I was kind of hoping someone could explain what the...

Oh...and I would just like to point out how the book does this type of problem. Seems incredibly non-intuitive to me. Let x \in ℝ. If x^{5} -3x^{4}+2x^{3}-x^{2} +4x - 1 ≥ 0, then x ≥ 0. Proof. Assume that x < 0. Then x^{5} < 0, 2x^{3} < 0, and 4x < 0. In addition, -3x^{4} < 0 and -x^{2}...

Still not entirely sure if I did it correctly...this class is giving me such a headache. Not sure if its the book or just my lack of understanding but some of these topics covered are going straight over my head... Let x\inℝ. If 3x^{4}+1 ≤ x^{7} + x^{3}, then x > 0. Proof...

Would it be because both powers of x are odd, which will mean it is always negative? So proving the contapositive would be an easier route than a direct proof?

Homework Statement Let x \in ℝ Prove that if 3x^{4}+1≤x^{7}+x^{3}, then x > 0 Homework Equations None The Attempt at a Solution Assume 3x^{4}+1≤x^{7}+x^{3} then 0 ≤ -3x^{4}-1≤x^{7}+x^{3} Then I assumed that each was greater than or equal to 0, which I thought gave the desired...

Homework Statement For a real number r, define A_{r}={r^{}2}, B_{r} as the closed interval [r-1,r+1], C_{r} as the interval (r,∞). For S = {1,2,4}, determine (a) \bigcup_{\alpha\in S} A{_\alpha} and \bigcap_{\alpha\in S} A{_\alpha} (b) \bigcup_{\alpha\in S} B{_\alpha} and...

I recently obtained a copy of Spivak' Calculus edition 3 and started going through the book. I've found that there is more than one way to prove what he is asking in his problem set and I'm wondering if this is a problem as to how he is trying to teach the subject? I would think not, but I'd...