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 Feb 4 answered Suppose $P(|X| < 1) = 1$ and $P(|Y| = 2) = 1$. Jan 26 reviewed Approve Solving limits with powers of x Jan 20 comment Exponential and Logarithmic Functions: $y=2e^{-5x^2}$ Draw the graph to get an idea. It answers majority of the questions by itself. And see then how the first and second derivative tests give the same results. Jan 10 comment an isomorphism from $L^\infty(\mathbb{T})$ to $L^\infty([-1,1],\displaystyle\frac{2}{\pi } \sqrt{1-t^2}\mathrm{d}t)$ What is the question? Jan 7 comment Sum of the sets in $\mathbb R^2$ Compact + closed = closed. So (c) is closed with X or with Y. Jan 6 awarded Yearling Dec 30 comment Proper solution of the limit of $\sin(x)/\tan(x)$ as $x \to 0$ This looks perfectly formal to me. By definition tan=sin/cos Dec 10 comment Prove $\operatorname{dist}(\overline{A},\overline{B}) = \operatorname{dist}(A, B)$ @ArielMarceloPardo: Infimum is an increasing function when you decrease the set of which the infimum is taken over. The intuition is that the smaller set has at least the same infimum as the ambient set, but possibly larger in case you remove the smallest values of the set when creating the subset. Nov 19 comment Optimizing a convex combination @michael. I know there is no answer in general, it's easy to produce counter examples even in $\mathbb{R}$, but it's also easy to find classes of functions for which it is possible, if the assumptions are strong enough. In the question I was asking for reference to literature where such problems are addressed, unless someone knows from the top of their head. Also, regarding Benjamin's post, each function is fully dependent on the same variable, most likely some nice function space in the context of my interest or the hilbert cube. But we definitely don't have an inner product in the domain. Nov 19 comment Optimizing a convex combination @michael. Yes. The supremum will be finite and the maximum will exist with quite mild assumptions. But I would like the maximizer to be some nice function of $x_i$, if that's possible. Nov 19 revised Optimizing a convex combination added 11 characters in body Nov 19 comment Optimizing a convex combination @BenjaminLindqvist. Not sure what you mean by that. Each $f_{i}$ is a function of the same variable. I've edited this to the question to make it more clear. This variable could be another function, a sequence of functions, a sequence of numbers, or anything else. We can assume that $X$ is a vector space for simplicity or a convex subset of such. Nov 18 comment Optimizing a convex combination @Surb: That is exactly the question: what properties would we want to require from each function $f_i$. I'm sure there are many different options, but if there is any literature that discusses this scenario, or if someone knows from the top of their head, I would really appreciate the input. Nov 18 asked Optimizing a convex combination Aug 13 reviewed Approve A fashion victim puzzle Aug 13 reviewed Approve What techniques would be use to prove $6x^2 +12x +8$ cannot be perfect cube for integer x > 0 Aug 7 comment How to find eigenvalues of matrix $\begin{bmatrix} 3& a+1\\a+1&3 \end{bmatrix}$ Have you calculated the determinant of that matrix? Aug 6 reviewed Approve From Hopf Algebras to quantum groups Aug 6 reviewed Reject Question of Differentiation/Integration Aug 4 reviewed Approve How can I write Klein bottle as an adjunction space?