The absolute-value tag has no wiki summary.
4
votes
2answers
182 views
Why isn't this square root $+$ or $-$?
I was tasked with proving the identity $\tan(\frac x 2) = \dfrac {\sin(x)}{1+\cos(x)}$
I used the quotient identity for tangent and the half angle identities for sine and cosine to get $ \pm \dfrac ...
2
votes
4answers
116 views
the solution set of $\left | \frac{2x - 3}{2x + 3} \right |< 1$
what is the solution set of $\left | \frac{2x - 3}{2x + 3} \right |< 1$ ?
I solved it by first assuming: $-1 < \frac{2x - 3}{2x + 3 } < 1$
ended with: $x > 0 > -3/2$
Is that a ...
2
votes
2answers
232 views
Expectation Values inside absolute value operator
first: are these equality true ?
$$|E[Y]-E[X]|=|E[Y]|-|E[X]|.$$
$$|E[Y]-E[X]|^2=|E[Y]|^2-|E[X]|^2$$
second: what is result of this relation:
$$\sum_{i=1}^{3}p_i.(X_i-\mu)^2=?$$
where the $\mu ...
0
votes
1answer
52 views
plotting the following set of points in the XY plane
Represent the following set of points in the XY plane :
$$\{ ( x , y ) \; | \; |x| + |y| = 1 \}$$
What i got:
1) if $x > 0, y > 0 : x = 1 - y$
2) if $x > 0, y < 0 : x = 1 + y$
3) if ...
0
votes
2answers
91 views
solving absolute value equation 2
My question is : Solve simultaneously-
$$\left\{\begin{align*}&|x-1|+|y-2|=1\\&y = 3-|x-1|\end{align*}\right.$$
I tried to solve this question by the method told by Marvis as I had ...
2
votes
3answers
145 views
Solve an absolute value equation simultaneously
My question is :
Solve simultaneously
$$\left\{\begin{align*}&|x-1|-|y-2|=1\\&y = 3-|x-1|\end{align*}\right.$$
What I did :
$y=3 - |x-1|$ is given.
Thus $y = 3-(x-1)$ or $y = ...
0
votes
2answers
84 views
about solving: Absolute value
How to solve: $|\sqrt{x-1}-2| + |\sqrt{x-1}-3|=1$.
I would like to know how to solve an absolute value equation when there is a square root sign inside.
0
votes
2answers
115 views
Solving $|x-2| + |x-5|=3$ [duplicate]
Possible Duplicate:
How could we solve $x$, in $|x+1|-|1-x|=2$?
How should I solve:
$|x-2| + |x-5|=3$
Please suggest a way that I could use in other problems of this genre too
Any help ...
0
votes
3answers
102 views
Absolute value on a number line
Solve : |x-4|>a if case1:a>0 and case2:a<0
I am getting answers which look similar in both cases.
please i wish to know why it is so and how different both answers are when plotted on a number ...
0
votes
1answer
130 views
Absolute value of a real number
My question is:
Solve: $|x-4|< a$, where $a$ belongs to the real numbers. Solve this by considering various cases depending upon whether $a$ is negative, positive or zero.
What I have tried ...
1
vote
2answers
99 views
Equality with absolute values - Is this a valid solution?
For this problem
$|2 - |x-2|| = 2$
I've found the values $x = -2$ and $x = 2$. However, an third solution was presented to me, which I can't seem to find by myself: $x = -6$.
Is this solution ...
0
votes
1answer
259 views
How to manage the absolute value on a differential equation $|T(x)'+A(T,x)+B(T,x)| = f(T,x)$
Hi everyone I need to solve an equation of this type:
$|T(x)'+A(T,x)+B(T,x)| = f(T,x)$
with boundaries conditions.
The absolute value is my problem. Of course without it, the solution of these is ...
0
votes
2answers
81 views
Two Analysis Questions
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) ...
1
vote
1answer
258 views
Finding the absolute extreme values for a multivariable function
Find the absolute extreme values taken by $f(x,y) = x^2 + 4y^2 + x - 2y$ on the closed region enclosed by the ellipse $1\over4$$x^2 + y^2 = 1$.
I know this might be a basic question but could ...
3
votes
6answers
299 views
Evaluating $\int |x|^3 \; dx $
$$\int |x|^3 \; dx $$
In my module it is suggest to use integration by parts,
$$ \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$$
...
1
vote
1answer
178 views
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.$
0
votes
2answers
122 views
I can't find a absolute value function that have [-1,1] range
I want a function $f:\mathbb{R}\to[-1,1]$ with absolute value like $f(x)=|a-x|\ldots$ that have $[-1,1]$ range. Can anybody help me?
0
votes
2answers
188 views
Math Database For Problem Descriptions In An App.
I am developing an app for kids and they will have a variety of problems from percentage problems, absolute value problems, negative number problems, fraction problems, etc. I was hoping to have a ...
1
vote
2answers
169 views
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 ...
0
votes
5answers
165 views
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 ...
1
vote
1answer
9k views
Integral of an absolute value function
How do I find the definite integral of an absolute value function?
For instance: $f(x) = |-2x^3 + 24x|$ from $x=1$ to $x=4$
0
votes
0answers
51 views
Name for $\max(x, \frac 1x)$, $x > 0$? [duplicate]
Possible Duplicate:
Multiplicative Identity analog for absolute value
In looking for the most extreme scaling, I'm comparing $f(a)$ and $f(b)$ where $f(x) = \max(x, \frac 1x)$, $x > 0$? ...
0
votes
1answer
59 views
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 ...
1
vote
2answers
111 views
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 ...
1
vote
0answers
76 views
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 ...
2
votes
1answer
272 views
How to manipulate absolute values when shifting parts in an inequality
I have the following inequality... $|4x - 2| \le 0.5$
I want to manipulate this so it is just $|x|$ on one side, and everything else on the other, but I'm not sure how the absolute value complicates ...
2
votes
2answers
311 views
How to minimize an equation with absolute values?
How would I go about minimizing the expression
$\left(|z_1| + |z_2|\right) \times \left(|z_1 + z_2| + |z_1 - z_2|\right)$
subject to the constraint
$|z_1|^2 + |z_2|^2 = 1$
given that $z_1$ and ...
-4
votes
1answer
234 views
Absolute Value theory [closed]
Could someone explain me the basics about absolute value? Not only how to solve it, but also the theory and the demonstration of theorems about it.
0
votes
6answers
274 views
How could we solve $x$, in $|x+1|-|1-x|=2$?
How could we solve $x$, in $|x+1|-|1-x|=2$?
Please suggest a analytical way that I could use in other problems too like this $ |x+1|+|1-x|=2$ and of this genre.
Thank you,
1
vote
1answer
153 views
How to solve equations with absolute value and using the Archimedean property
I'm trying to learn Real Analysis on my own, but I found that i'm a bit rusty with the elementary stuff.
How do I solve equations like $|x| + |x+1| = 1$ and $|x-1| + |x+1| = 2$? I don't want the ...
0
votes
5answers
164 views
Solving an equation with absolute values
The equation I am trying to solve is this : $\newcommand\abs[1]{|#1|}\abs{3y+7}=\abs{2y-1}$.
My conventional approach is to split this into three intervals with $1/2$ and $-7/3$ being the two "split" ...
0
votes
2answers
70 views
Domains and setbuilder notation
We're learning about domains and setbuilder notation in school at the moment, and I want to make sure what I did was right.
My thought process:
\begin{align*}
-\frac12|4x - 8| - 1 &< -1 \\
...
0
votes
1answer
372 views
derivative of absolute value of a complex function
If $f:U\subset\mathbb{C}\mapsto\mathbb{C}$, where $f(x+iy)=u(x,y)+iv(x,y)$ is a meromorphic function and if $f$, $f'$, and $f''$ are not zero in the strip $a<x<b$, can we get ...
1
vote
1answer
2k views
Limit with absolute value
I found this limit within the Calculus Single Variable book from Thomas.
$$ \lim _{x \to -2^-} (x+3) \frac{|x+2|}{(x+2)}$$
This is how I'm trying:
First of all, we need to found where the absolute ...
4
votes
1answer
520 views
Prove variant of triangle inequality containing p-th power for 0 < p < 1
Sorry if this is a trivial question, but I am kind of stuck with proving the following inequality and have been searching for a while:
$\rho \left( \sum\limits_i^n d_i \right) \leq \sum\limits_i^n ...
3
votes
1answer
256 views
Why do definitions of distinct conic sections produce a single equation?
I understand how to get from the definitions of a hyperbola — as the set of all points on a plane such that the absolute value of the difference between the distances to two foci at $(-c,0)$ and ...
2
votes
1answer
228 views
When should I put an absolute value sign around a function?
In Griffiths' introduction to QM book, I see $\int f^* f\ dx$ often written as $\int | f |^2 dx $, whereas $\int f^* g\ dx$ is understandably just that. Should I always write the absolute value sign ...
0
votes
2answers
249 views
Joint pdf of X and Y with absolute value range
I have the following joint pdf:
$f(x,y)=0.5$ where $0 \leq|x|\leq|y|$, $0 \leq|y|\leq1$, and $0$ otherwise
The question is: are $X$ and $Y$ independent and uncorrelated?
I know that if ...
2
votes
2answers
80 views
How do I find this limit?
How would i find the limit as $\lim\limits_{x\to3}\frac{4x(x-3)}{|x-3|}$? that is the absolute value of x-3 in the denominator. I thought my professor told my class that we were able to omit the ...
2
votes
1answer
111 views
$|x-y| + |y-z| = |x-z|$ then $x \le y \le z$
I'm doing this exercise from Robert Bartle's Introduction to Analysis, it's a if only if excersise and I've done the half part, but I can't figure this part of the ...
3
votes
2answers
240 views
Why exactly can you take the absolute value of one side of this inequality and assume it is still true?
Exercise:
Show that if $(b_n) \to b$, then the sequence of absolute values $\left| b_n \right|$ converges to $\left| b \right|$.
Solution (partial):
By the triangle inequality, ...
3
votes
1answer
102 views
Inequality with absolute value
I am unsure if have solved the following inequality correctly:
$ \dfrac{2x+3}{x+5} \leq \dfrac{x+1}{|x-1|} \tag{1}$
I've proceeded as follows.
If $x>1$ then $|x-1|=(x-1)$
If $x<1$ then ...
3
votes
1answer
438 views
Proving Absolute Value Inequality
I had posted a portion of this earlier asking about how to interpret min(). I received some excellent answers, however, I have run into problems and feel stuck. I am posting the question in its ...
4
votes
1answer
304 views
integral from 0 to $2\pi$ of $|\cos x|\operatorname{d}x$ not integrating as I'd expect
I drew a rough sketch of $|\cos x|$ and would guess the correct answer to this integral is $4$ because I know the area under the curve of $\cos x$ from $0$ to $\pi/2$ is $1$, and there are $4$ such ...
3
votes
3answers
111 views
Solving $ \left| \frac{-2x-6}{4} \right| \le 5$ for $x$
Say I have a statement like:
$$
\left| \frac{-2x-6}{4} \right| \le 5.
$$
And I want to find the closed interval form of $x$. i.e. I want to know what the maximum and minimum $x$ can be. How do I ...
2
votes
2answers
1k views
Square root of simple binomial function
Let's say I have the following formula:
$$\sqrt{a^2-2ab+b^2}=\sqrt{(a-b)^2}=\sqrt{(b-a)^2}$$
When do I know which one of the following I should use?:
$$\sqrt{(a-b)^2}=a-b\qquad\text{ or }\qquad ...
5
votes
2answers
639 views
How to use triangle inequality to establish the following one
I need to use $|a+b| \leq |a|+|b|$ to show that $||a|-|b|| \leq |a-b|$. I have tried to represent $||a|-|b||$ as $||a|+(-|b|)|$, and then get $||a|+(-|b|)| \leq |a|+|-|b||$, but that isn't leading ...
2
votes
1answer
209 views
Rules applying to nested absolute values
I'm trying to use some algebra get $||x-5|-10|<\epsilon$ into a more manageable form (I'd like it in terms of $0<|x+5|<\delta$) but I'm not sure where to begin. I don't really know the rules ...
2
votes
3answers
327 views
Trouble with absolute value in limit proof
As usual, I'm having trouble, not with the calculus, but the algebra. I'm using Calculus, 9th ed. by Larson and Edwards, which is somewhat known for racing through examples with little explanation of ...
8
votes
5answers
435 views
Is -5 bigger than -1?
In everyday language people often mix up "less than" and "smaller than" and in most situations it doesn't matter but when dealing with negative numbers this can lead to confusion.
I am a mathematics ...
