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 Nov 2 comment Extended version of Mean-Value Theorem, lower bound result and reference request. @DanielFischer This is a counter example ? If $f (x, y) = e^x (\cos y, \sin y)$ then there not exists $m> 0$ and $M> 0$ such that $m<\|Df(x)\|_{\mathscr{L}(\mathbb{R}^2,\mathbb{R}^2)} 0$, does that imply the limit as $x\rightarrow \infty$ is $\infty$? This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. Oct 3 comment Improving Newton Iteration This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. Oct 3 comment Prove that $\lim \limits_{n \to \infty}{\sqrt[n]{a^n+b^n}}=\max(a,b)$ if $(a_n,b_n)\to(a,b)$ Possible duplicate of How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$? Sep 5 comment How strong is the operator norm topology? Your comment this makes your question more precise and interesting. I suggest incorporating this enlightening comment to your question. Sep 5 comment How strong is the operator norm topology? What do you mean exactly by "how strong is the topology T"? Jul 7 comment Can there be generalization of Monty Hall Problem? Jun 8 comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$ @RoryDaulton I do not want to be rude. But if it is not proved the convergence of the sequence $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ to $f(x)=0.25^x+0.5^x+0.75^x-1$ and $x_0 = 1.5$ converge then your answer is not correct. Jun 8 comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$ @RoryDaulton Another point which I understand is that you are assuming tacitly that if the method of bisection converges then Newton-Raphson method converge. You really mean it? Jun 8 comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$ @RoryDaulton I think that to ensure convergence should use some type of Kantorovich's theorem for Newton methold to ensure the convergence of the sequence obtained by Newton's menthold. Jun 8 comment Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$ @Rory Daulton It is necessary to prove that the sequence which is obtained from the Newton-Raphson method converges when $x_0 = 1.5$. May 25 comment Dvoretzky–Kiefer–Wolfowitz inequality holds for discrete distributions? What is your attempt to deal with the problem? You searched examples or counterexamples? May 2 comment Number of circuits that surround the square. see also another related question here. May 2 comment The problem of the most visited point. see also another related question here. Apr 27 comment Why $\int_{\mathbb R^n}e^{-\sum_{i=1}^n x_i^2} \, dx_1\cdots dx_n=\omega_{n-1}\int_0^\infty e^{-r^2}r^{n-1} \, dr$ Did you mean that $\sum_{i=1}^1 x_i^2=1$ rather than $\sum_{i=1}^1 x_i=1$ ? Apr 27 comment Why $\int_{\mathbb R^n}e^{-\sum_{i=1}^n x_i^2} \, dx_1\cdots dx_n=\omega_{n-1}\int_0^\infty e^{-r^2}r^{n-1} \, dr$ Did you mean that $\omega_{n-1}$ is the area of surface rather than $\omega_{n-1}$ be the surface? Apr 2 comment Number of circuits that surround the square. @DavidHolden +1 Yes. That's why we could not solve the problem with this strategy. But at least I can get a lower bound for the number of circuits. And I think with some trick I improve my lower bound. Mar 27 comment proving gradient of a scalar field is perpendicular to equipotential surface This question and this answer can give you too a direction:math.stackexchange.com/questions/401845/… Mar 27 comment Why gradient vector is perpendicular to the plane See this question and may answer: math.stackexchange.com/questions/401845/…