0
votes
4answers
53 views

solving the system

solve the system : $$ y+|x-2|=3 $$, $$ |x+y|= m $$ graphicly when $m$ equals $6$. I can easily (realtively) skecth the first graph , however, how the bloody hell do you sketch $|x+y|= 6$??
3
votes
4answers
237 views

inequality method of solution

Im looking for an efficent method of solving the following inequality: $$\left(\frac{x-3}{x+1}\right)^2-7 \left|\frac{x-3}{x+1}\right|+ 10 <0$$ I've tried first determining when the absolute value ...
2
votes
3answers
178 views

Derivative and integral of the abs function

I would like to ask about how to find the derivative of the absolute value function for example : $\dfrac{d}{dx}|x-3|$ My try:$$ f(x)=|x-3|\\ f(x) = \begin{cases} x-3, & \text{if }x \geq3 \\ ...
3
votes
3answers
77 views

Please help with absolute value $|x^2 - 3x| = 28$

Just a question about solving an absolute value equation: $$|x^2 - 3x| = 28$$ Do I just solve this as if the absolute value brackets weren't even there? $$x^2 - 3x - 28 = 0$$ $$(x+4)(x-7) = 0$$ ...
0
votes
1answer
17 views

Modulus function (working out coordinates)

Lets say you have $y = -|3x - 1|$ when working out where it cuts the axis, particularly the x-coordinate you do the following when $y = 0, 3x - 1 = 0$ therefore $x = 1/3 $ the modulus and the ...
0
votes
1answer
50 views

Integral of absolute value = absolute value of the integral

Let $(a,b) \in \mathbb{R}^2$ and $f \in C^0([a, b] , \mathbb{C})$ Find the condition on $f$ so that $$|\int_a^b f|=\int_a^b|f|$$ My try : The function $f: t \mapsto r(t)\exp(i\theta)$ where $r$ is a ...
0
votes
3answers
23 views

What's the best method to graph the following function by hand…

Here in my exercise I have to study the function and draw its graph. Can you please tell me what's the best method to do this, because I don't think that's reasonable to use the input output method, ...
1
vote
0answers
51 views

Absolute values nested multiple times

Is there any algorithm to quickly determine "zero points" (i.e. points with undefined derivation) of absolute values functions which are nested multiple times? I do know, that any part of this ...
0
votes
1answer
48 views

Solve the following inequality…

Can you please verify if I've done this exercise correctly, and if you have a better solution, please, show it to me. Thank you! (The exercise is in the left top corner.)
2
votes
1answer
25 views

Real parameter equation

I'm having a problem with this question: For which values of the real parameter a the equation: $$||x|-1|=a$$ has exactly 4 solutions? The solution is this: $$0 < a < 1$$ What I tried was ...
0
votes
2answers
21 views

Determine a value $t_0$ such that $|u(x,t)| = |-4e^{-2t/5}\cos2x\;| < 0.0001$

My problem is the following: Determine a value $t_0$ such that $|u(x,t)| = |-4e^{-2t/5}\cos2x\;| < 0.0001,$ for $t > t_0$, with $0<x<\pi$. How to approach this problem? According to my ...
0
votes
1answer
176 views

Logarithmic inequalities

Full disclosure: This is a homework problem, but my question is regarding a concept that came about during solving the problem, not the actual solution to the problem. Problem: Rewrite as geometric ...
0
votes
1answer
64 views

Absolute value and credit card balance

I'm embarrassed to ask this question, but my child has the following homework question: "Use absolute value to describe the relationship between a negative credit card balance and the amount owed." ...
3
votes
3answers
107 views

Proving continuity of a absolute value function

How can i prove the function $f: x \mapsto x|x|$ is continuous over $\mathbb{R}$ using epsilon-delta definition. I've tried: Given a certain $\epsilon$ we want to prove that there exists a $\delta$ ...
-4
votes
3answers
68 views

How to solve this: $|3-x|\ge2$

How to solve $|3-x|\ge2$ ? I know that if $|x| < y$, then $-y < x < y$. But in this case what to do? Thanks. Here, $|x|$ is the absolute value of $x$.
0
votes
1answer
63 views

usage of absolute value within natural log in solution of differential equation

y=2^x sinx rewriting, |y|=2^x |sinx| my questions, before taking the natural log for both sides and rearrange why do we need to rewrite using absolute value? why this particular question need to have ...
0
votes
4answers
70 views

Inequalities and absolute values

My book asks that if $$-5\leq x\leq 1$$ then find the boundaries of absolute value of $x$. Can you please help me in finding that?
0
votes
1answer
52 views

Algebra Absolute Value

Let $a,b,c$, and $d$ be real numbers with $$|a-b|=2, \hspace{.2in} |b-c|=3, \hspace{.2in} |c-d|=4$$ What is the sum of all possible values of $|a-d|$? I am completely clueless on how to begin! It's ...
2
votes
1answer
83 views

what is the value of $a+b?$

Can anyone help me to solve this problem: $x$ and$y$ are real numbers which satisfy $x>y$ and $xy<0$. If $\left | x \right | + \left | y \right | + \left | 42y-x \right | + \left | 23x-y \right ...
2
votes
2answers
124 views

Under what conditions is the identity |a-c| = |a-b| + |b-c| true?

As the title suggests, I need to find out under what conditions the identity |a-c| = |a-b| + |b-c| is true. I really have no clue as to where to start it. I know that I must know under what ...
1
vote
3answers
72 views

Value and simplify

I want to find the value and simplify square root 36 ? Square root of 36 is 6 But I would know how to find the value and simplify it .
0
votes
1answer
2k views

Chain rule and the derivative of absolute value functions

Is it possible to use the chain rule to calculate the derivative of $|x^4|$ and $|x|^4$ in $x=0$? Does the derivative to these functions exist in $x=0$?
1
vote
1answer
2k views

Normal distribution with absolute value

I am new to the normal distribution topic. While I have understood and solved various different kind of questions, the normal distribution questions with absolute value, are the ones I have no idea ...
0
votes
2answers
101 views

How to solve $|2x +1|< 1/4$?

How do you solve $$|2x +1|< \frac{1}4$$
1
vote
3answers
121 views

Inequalities - Absolute Value

$$|2x-1| \leq |x-3|$$ Answer is $$-2 \leq x \leq \frac43$$ My Question is HOW?
1
vote
2answers
156 views

Graphing - Absolute Value and Circle

The diagram Shows The Graphs of $y = |x + 2|$ and $y = \sqrt{4 - x^2}$ Write down the solution for $\sqrt{4 - x^2}$ is equal to or less than $y = |x + 2|$.
12
votes
6answers
892 views

Show that the $\max{ \{ x,y \} }= \dfrac{x+y+|x-y|}{2}$.

Show that the $\max{ \{ x,y \} }= \dfrac{x+y+|x-y|}{2}$. I do not understand how to go about completing this problem or even where to start.
3
votes
1answer
124 views

Question based on Triangle Inequality $\displaystyle |x+y|\leq |x|+|y|$

If $x,y,z\in \mathbb{R}-\left\{0\right\}$. Then prove that $\displaystyle 1\leq \frac{|x+y|}{|x|+|y|}+\frac{| y+z|}{| y |+| z |}+\frac{| z+x|}{| z |+| x |}\leq 3$ My Try:: Using Triangle Inequality ...
0
votes
2answers
76 views

Absolute Value Problem, Solution and Method

Please check my method and also if I have solved the following problem correctly: Problem: $f(x) = |x - \frac12| + |x + \frac12|$ If $x = -1$, then: $f(-1) = |-1 - \frac12| + |-1 + \frac12|$ From ...
2
votes
2answers
64 views

proving $|x - 1| < {1\over4} \Rightarrow |2x - 1| \geq {1\over 2}$

I tried solving the above, consider that: ($x \in R)$, I know it's not a complicated problem to solve though I struggle getting on with this question, What I've done far is: $|x-1|<{1\over4} ...
1
vote
3answers
67 views

Find $x$ for absolute value inequalities

I'm trying to figure out this inequality: $|x+1| + |x| \leq x^2$ I thought about trying it with two cases: $ (x = -x)$ and $(x = +x)$ but I don't seem to find out how to go through from here, ...
0
votes
1answer
97 views

Finding The Contour Maps Of A Function Of Two Variables

I am given the function $f(x,y) = \ln|y-x^2|$, and am suppose to find the contour maps. Let $z = c = f(x,y)$. $c = \ln|y-x^2| \rightarrow e^c = e^{\ln|y-x^2|} \rightarrow e^c = |y-x^2|$ I know I ...
1
vote
1answer
3k views

Finding the points of the curve where the tangent line is horizontal

The curve given is $\displaystyle y = \ln|x-2| + x + \frac{12}{x-2}$. Find the points of the curve where the tangent line is horizontal. My first stumbling block is the absolute value function. I ...
6
votes
2answers
1k views

Question regarding usage of absolute value within natural log in solution of differential equation

The problem from the book. $\dfrac{\mathrm{d}y}{\mathrm{d}x} = 6 -y$ I understand the solution till this part. $\ln \vert 6 - y \vert = x + C$ The solution in the book is $6 - Ce^{-x}$ ...
1
vote
4answers
213 views

Truth set of $-|x| \lt 2$?

An exercise in my Algebra I book (Pearson and Allen, 1970, p. 261) asks for the graph of the truth set for $-\left|x\right| \lt 2; x \in \mathbb{R}$. I've re-stated the inequality in the equivalent ...
1
vote
2answers
159 views

When does a absolute value equation have one unique solution?

Find $m \in \mathbb R$ for which the equation $|x-1|+|x+1|=mx+1$ has only one unique solution. When does a absolute value equation have only 1 solution? I solved for $x$ in all 4 cases and got ...
1
vote
2answers
74 views

Confusion solving $\sqrt{4m^2-4m+1}+|1-2m|\leq2$, weird solution.

I am trying to solve $\sqrt{4m^2-4m+1}+|1-2m|\leq2$. Since i know $|1-2m| = \pm(1-2m)$ i tough solving $\sqrt{4m^2-4m+1}+1-2m\leq2$ and $\sqrt{4m^2-4m+1}-1+2m\leq2$. As solutions i get $0\leq2$ and ...
1
vote
2answers
93 views

How to prove this inequality $x,y\in\Bbb R$, $|x|<1,|y|<1$ show that $\bigg|\frac{x-y}{1-xy}\bigg| < 1$ (and similar ones)

I have to show that the inequality below is true, i tried some thing but got stuck, i tried to eliminate the absolute value $-1<\frac{x-y}{1-xy}<1$ and then solve for $x$ and $y$ with no ...
5
votes
1answer
121 views

An absolute value problem

Let $a$ and $b$ in $\mathbb{R}$ 1) Show that $||a|-|b||\leq|a+b|\leq|a|+|b|$. 2) Prove that the one or the other of the two inequalities is an equality. It's fine whit the 1st question but i can't ...
4
votes
2answers
207 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 ...
0
votes
2answers
110 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 ...
0
votes
3answers
110 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
170 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 ...
2
votes
2answers
491 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 ...
1
vote
1answer
542 views

Prove by contradiction or contrapositive? If $|x+y|<|x|+|y|$, then $x<0$ or $y<0$.

Prove: If $|x+y|<|x|+|y|$, then $x<0$ or $y<0$ This looks as though it's true from the start. Take $x=-4, y=4$. $|-4+4|<|-4|+|4|$ $0<8$ is true. The question is asking for a ...
2
votes
1answer
130 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 ...