# Tagged Questions

For questions about or involving the absolute value function.

19 views

### Absolute Value Graph Problem in Gelfand's Functions and Graphs

I am working through Gelfand's Functions and Graphs, where I am currently on the absolute value section. At the end of the chapter practice problems, Gelfand poses a set of problems regarding ...
45 views

### Calculation double Integral over Ball (optical size)

I hope that someone can help me with the following problem. I have to show that $$\int_{B_1(0)}\int_{B_1(0)}\frac{1}{|x-y|^2}dxdy=4\pi^2~,$$ with $B_1(0)\subset\mathbb{R}^3$. I have no idea how to ...
40 views

### Inequality with two absolute value

How can you tackle an inequality problem that has two absolute values? Example is the following $p + |k| > |p| + k$ and the questions is a quantitative comparison between A) $p$ B) $k$ The ...
21 views

### Is following a norm or absolute value of a vector?

I'm reading a paper regarding power minimization and came across with following equation: $g_{i,j}=|h_{i,j}|^2/d^\alpha$ Where $h_{i,j}$ is a complex vector of dimension $N$. I don't know and it ...
83 views

### Is there any clever way to solve inequalities like $|y^2-y-2|\geq 4 + |y^2+y-2|+|y+4|+|y|$?

I have to solve different types of inequalites of this type: $$|y^2-y-2|\geq 4 + |y^2+y-2|+|y+4|+|y|$$ I know the standard method for solving these inequalities, by finding the all zeros of the ...
32 views

129 views

### Why there is no value for $x$ if $|x| = -1$? [duplicate]

According to the definition of absolute value negative values are forbidden. But what if I tried to solve a equation and the final result came like this: $|x|=-1$ One can say there is no value for $x$...
83 views

63 views

49 views

### A question about the absolute value in integrals

I do really understand why we put the absolute value when integrating functions leading to $\log$ function for example: $$\int{\dfrac{\mathrm dx}x}=\log\lvert x\rvert + C$$ , it is very common in ...
53 views

31 views

### Integrals of a function and its absolute value

Is the following proposition true? Let $f(x)$ be a real-valued function defined on $[a,b] \subset \mathbb{R}$, and suppose that the integral, $$I = \int_a^b f(x) dx,$$ exists in the sense of ...
40 views

### Joint pdf of X and Y with absolute value

Question. Joint probability function of continuous probability X, Y is here : $f_{X,Y}(x,y) = k(|x|-|y|) \ \ \ \ \ \ \ \ \ \ (-1< y< x< 2)$ Then what is k? I mean how can I differentiate ...
105 views

### How to minimize $|Ax+By + C|$ given that $x \geq 0$ and $y\geq 0$ [duplicate]

I am trying to solve problem related to absolute value function, i.e given $Z(x,y) = |Ax + By + C|$ , what is the minimum value of $Z$, if $x \geq 0$ and $y\geq 0$ and x,y belongs to integers
112 views

37 views

### How to solve this problem on absolute value function?

If $a,b\in \mathbb R$ and be distinct numbers satisfying $$|a-1|+|b-1|=|a|+|b|=|a+1|+|b+1|$$ then the minimum value of $|a-b|$ is ? ($|...|$ represents absolute value) I tried solving the equalities ...