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 2d comment Conditional Expectation and Conditional Variance of die Like @Siron I'd break it into cases (Siron is absolutely correct, but sort of takes a shortcut) 2d comment Comparing two functions asymptotically I'm curious: what makes you think $f$ is the slower function? 2d comment How to apply the Implicit function Theorem in multi-variable Calculus I'm not sure about the implicit function theorem, but do you know about implicit differentiation? (they might be the same thing) Apr 18 comment solving for the phase plane equation help? In this specific case, if you differentiate dx/dt again you get 2*dy/dt - dx/dt = 2*(e^x+y) - (2y + x) = 2*e^x + x. By integrating twice and figuring out constants, I think you can solve x(t) explicitly. Apr 18 comment solving for the phase plane equation help? I like this answer because I can pretend it's what I said (and it sort of is, but written much better than I wrote it). Apr 18 comment solving for the phase plane equation help? OK, this doesn't answer your question, but remember than x is a function of t, and y is a function of t, so x is implicitly a function of y and vice versa. In other words, when you integrate x dy you don't get x y, because x is a function of y, not a constant. In this case, try taking the mixed partial with respect to t for both parametric equations and setting them equal (not sure that'll work, but maybe). Apr 18 comment Given that $\sum\frac{1}{n^2} = \frac{\pi^2}{6}$, how can I find $\sum\frac{1}{n^6}$? My thought would be to start with the infinite series of 1/(1-x) and manipulate until I had this. Not sure it will work, but it may. Apr 18 comment solving for the phase plane equation help? When you integrate in this way, you must have all y's on one side and all x's on the other side. You can't mix and match as you do in several of the cases above. Apr 15 comment Optimization question related to calculus. This problem would be more interesting if a^2+b^2 = c and you were maximizing a+b (still not difficult, but more interesting). Apr 7 comment Using generating functions to count Thought: remember that 123456 is 10^5 + 2*10^4 + 3*10^3 ... (not sure if that helps) Apr 7 comment Countable Choice And Countable Union Of Countable Sets Being Countable Meaning: given a collection of nonempty subsets of the natural numbers, you can always choose a given element? You don't need the Axiom of Choice for that: just choose the smallest element. Apr 7 comment If $n\in N$ and $f(x)=\ln(1+x^{2n})$, then derivative $f^{(2n)}(-1)=0$. Perhaps try induction? The derivatives should have some "regular" form. Apr 6 comment Gamma representation of certain sequence 15!! (long live the semi-factorial!) Apr 5 comment Irrational numbers generated by a deterministic cellular automaton? To resolve this, can we say we have a sequence of computable rational numbers whose limit converges to an irrational number? Apr 5 comment Prove that $[A\cup B^\complement\cap C\cup D^\complement]^\complement = A^\complement\cup B^\complement\cap C^\complement\cup D^\complement$ is false. Intersections are generally treated like multiplication and unions are treated like addition, which may help resolve the order of operations here. stackoverflow.com/questions/16805630/and-or-order-of-operations Apr 5 comment show that ∀ x P ( x ) ∨ ∀ x Q ( x ) is logically equivalent to ∀ x ∀ y ( P ( x ) ∨ Q ( y )) . (Domains for x and y are the same). In 2), how do you get that P(x) is false for all x, just because there is a single x0 for which P(x0) is false? It's possible that P(x0) is false, but P(x) is true for all x not equal to x0. Apr 5 comment Showing a parametrization of the ellipsoid Hint: consider v = 0 and v = Pi/2, but I suspect there's something wrong with your equations. Did you really mean to combine hyperbolic functions with trigonometric ones? One parametrization of an ellipse in 2 dimensions is (a cos(theta), b sin(theta)). I think you want something similar to this. Apr 5 comment Prove that optimal Solution exist without solving. You can substitute x1 and x2 and turn this into a simple two variable problem. Apr 5 comment Irrational numbers generated by a deterministic cellular automaton? @N74 Yes, but cellular automata like this continue forever. The OP has just shown the first few steps. With each new step, you get more digits. Apr 4 comment Calculating limit $\lim_{x,y\to \{0;0\} }(x^2+y^2)^{x^2 y^2}$ WolframAlpha is having some serious problems, so I wouldn't be surprised if it was wrong. However, could you provide us with a link to the WA result? My result agrees with yours, but it may be a directional issue.