# All questions with tag [math: absolute-value]

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## How to manage the absolute value on a differential equation $|T(x)'+A(T,x)+B(T,x)| = f(T,x)$

Hi every person I require to address a formula of this type: $|T(x)'+A(T,x)+B(T,x)| = f(T,x)$ with borders problems. The absolute value is my trouble. Certainly without it, the remedy of these is well dealt with in the literary works. After search in the inquiries I located this: So, can I do the very same procedure? Or there is an additio...
2022-07-25 20:41:51
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1) Define : $\langle z\rangle := (1+|z|^2 ) ^\frac{1}{2}$ for all $z \in \mathbb{C}$. Prove : $\langle x+y\rangle \leq 2\langle x\rangle\langle y\rangle$ for all $x,y \in \mathbb{R} ^N$ . 2) Define: $S^\beta := \left\ \leq c_n \langle x\rangle^\beta -n \right\$ for some $c_n&lt;\infty$, all $x \in \mathbbR$ and all $0\leq n \in ... 2022-07-25 15:57:04 1 ## Finding the absolute extreme values for a multivariable function Find the outright severe values taken by$f(x,y) = x^2 + 4y^2 + x - 2y$on the shut area confined by the ellipse$1\over4$$x^2 + y^2 = 1. I recognize this could be a standard inquiry yet could a person please clarify just how to address this trouble? Many thanks beforehand. 2022-07-24 09:23:44 3 ## Inequality absolute value If x&gt;0,y&gt;0, why does it adhere to for any kind of y \in (x,x+1), that from:$$|f(y)-f(x)|&lt;1,$$we have$$|f(y)| \leq |f(x)|+1$$2022-07-24 09:18:26 5 ## Evaluating \int |x|^3 \; dx$$\int |x|^3 \; dx $$In my component it is recommend to make use of integration by components,$$ \text{ Set }I = \int (|x|^3 \cdot 1) \; dx = |x|^3 \cdot x - \int \color{red}{\frac {x^3}{|x|^3}3x^2}\cdot x \; dx \implies I = |x|^3 \cdot x - \color{red}{3\int |x|^3\;} dx \implies I = \frac 1 4 |x|^3 \cdot x +C $$I am having probl... 2022-07-22 18:37:36 2 ## Integral of an absolute value I am attempting to review the indispensable$$\int_{-1}^2 (x-2|x|)\,dx$$I recognize that this need to offer me x^2 /2 - x^2 for the antiderivative. I after that review at 2 which offers me 2 - 4 = -2 Then review at -1 and also get \frac{1}{2} - 1 = -\frac{1}{2}. After that I locate the distinction -2 - \frac{1}{2} = -2.5 This i... 2022-07-22 15:31:14 1 ## The relationship between the derivative of f(x) and |f(x)| I have seen it in an exercise book. I don't know how to do it. If f(x) is continuous at x=a, and |f(x)| can be differentiated at x=a, then f(x) is differentiable at x=a. 2022-07-20 00:50:50 2 ## I can't find a absolute value function that have [-1,1] range I desire a function f:\mathbb{R}\to[-1,1] with absolute value like f(x)=|a-x|\ldots that have [-1,1] array. Can any person aid me? 2022-07-17 17:39:54 2 ## Math Database For Problem Descriptions In An App. I am creating an application for children and also they will certainly have a selection of troubles from percent troubles, absolute value troubles, adverse number troubles, portion troubles, etc I was wanting to have a summary of just how to do each type prior to they started. Does any person recognize of a good data source where I could get all... 2022-07-16 17:25:35 1 ## Prove that ||x|-|y||\le |x-y| I've seen the complete evidence of the Triangle Inequality \begin{equation*} |x+y|\le|x|+|y|. \end{equation*} However, I have not seen the evidence of the reverse triangular inequality: \begin{equation*} ||x|-|y||\le|x-y|. \end{equation*} Would you please confirm this making use of just the Triangle Inequality over? Thanks significantly. 2022-07-16 17:10:41 0 ## Smoothing of absolute value and sign functions for numerical integration I'm doing Numerical integration of ODEs. for a special system that has an always positive coordinate s and a conjugated momentum ps. At some point the equations become so stiff that s becomes negative and if I improve tolerances of the numerical integrator, it crashes. To solve this problem, I'd like to approximate the ODEs with s_new=abs(s) and... 2022-07-16 16:54:43 1 ## Integral of an absolute value function How do I locate the precise indispensable of an absolute value function? As an example: f(x) = |-2x^3 + 24x| from x=1 to x=4 2022-07-14 02:19:53 5 ## The solution set of the equation |2x - 3| = - (2x - 3) The solution set of the equation \left | 2x-3 \right | = -(2x-3) is A) 0 , \frac{3}{2} B) The empty set C) (-\infty , \frac{3}{2}] D) [\frac{3}{2}, \infty ) E) All real numbers The correct answer is C my solution: \ 2x-3 = -(2x-3) when 2x-3 \geqslant 0 \Rightarrow x = \frac{3}{2} -(2x-3) = -(2x-3) wh... 2022-07-14 01:24:34 3 ## The median minimizes the sum of absolute deviations (the  {\ell}_{1}  norm) Suppose we have actually a set S of actual numbers. Show that$$\sum_{s\in S}|s-x| $$is marginal if x amounts to the median. This is an example test inquiry of among the tests that I require to take and also I do not recognize just how to continue. 2022-07-10 04:54:04 1 ## Does the triangle inequality for the absolute value hold for matrix trace? It is well - recognized that, \left|m-n\right|\ge\left|\left|m\right|-\left|n\right|\right| genuine numbers. Yet if one specifies \left|M\right|=\sqrt{M^2} for a symmetrical matrix M, does one have$$\operatorname{trace}\left(\left|M-N\right|\right)\ge\operatorname{trace}\left(\left|\left|M\right|-\left|N\right|\right|\right)$$if M\ne\le... 2022-07-07 02:32:19 1 ## When is possible to ignore an absolute value e^{\frac{2}{x-1}\log\left|x-1\right|}+1\neq 0 Since that this is an exponential function, this equation is verified \forall x \in \mathbb{R}? Or I have to consider the absolute value of the ligarithm? Note: these are not homework. 2022-07-06 23:35:12 1 ## How to manipulate absolute values when shifting parts in an inequality I have the adhering to inequality |4x - 2| \le 0.5 I intend to adjust this so it is simply |x| on one side, and also every little thing else on the various other, yet I'm not exactly sure just how the absolute value makes complex points. Just how would certainly I deal with this? 2022-07-06 00:52:32 0 ## Fields with their own absolute value Let F\hspace{.02 in} be a field. \: Let E\hspace{.02 in} be a non-zero subring of F. Let \hspace{.03 in}\leq\hspace{.03 in} be a total order on E\hspace{.02 in} that makes E\hspace{.02 in} an ordered ring. \;\;\; Let \;\; |\cdot| \: : \: F\to E \;\; be a function. I will require the following to hold for all members x of E... 2022-07-06 00:36:30 2 ## How to set up the existence condition of an absolute value$$ \frac{\sqrt{4 + \arccos\left|\frac{2-x}{x+3}\right|}}{\sqrt{x^2 - 4x + 5} - 3} $$I'm trying to find the natural domain of the function above. I set up this conditions:$$ \begin{cases}\sqrt{x^2 - 4x + 5} - 3\neq0&amp;(denominator)\\x^2 - 4x + 5\ge0&amp;(root)\\4 + \arccos\left|\frac{2-x}{x+3}\right|\ge0&amp;(root)\\\left|\frac...
2022-07-06 00:13:05
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## How to minimize an equation with absolute values?

How would certainly I deal with decreasing the expression $\left(|z_1| + |z_2|\right) \times \left(|z_1 + z_2| + |z_1 - z_2|\right)$ based on the restraint $|z_1|^2 + |z_2|^2 = 1$ considered that $z_1$ and also $z_2$ can be intricate numbers? I considered attempting Lagrange multipliers, yet it does not appear feasible due to the fact that ...
2022-07-04 20:34:31