Absolute value Definition and 368 Threads

how do you go about solving abs value inequalities with double variables when the abs value bars are on both the variables? eg; |x| + or - |y| =, >, <, a

Homework Statement prove that llal-lbll\leqla-bl Homework Equations Triangle inequality lx+yl\leqlxl+lyl The Attempt at a Solution Let a=(a-b)+b By using the triangle inequality we get lal-lbl\leqla-bl Then from here I am not sure what I can do. I would like to say on the left...

Homework Statement Then find the area S of the region. (between the curves) Homework Equations A = \int_a^b f(x)-g(x) dxThe Attempt at a Solution First I plotted both equations, determined the top and the bottom functions and found where they intersected (calculator). Then I set up the...

Homework Statement l [3/(x-1)] - 5l < 4Homework Equations The Attempt at a Solution My 1st step was to make the inequality like this. -4 < 3/(x-1) - 5 < 4 and then i multiplied (x-1) to both left and right side and as well as to the 5. but in the end, my result turns out to be...

Homework Statement y= l sin x l < absolute value of sinx Homework Equations The Attempt at a Solution y= l sin x l= sinx, if x>0 -sinx, if x< 0 0, if x=0 I get that part, but when i draw the graph I don't get it

Homework Statement Solve (x+2)/(x+1) -2 < 0 Homework Equations LCD: x + 1 The Attempt at a Solution (x+2-2x-2)/(x+1) < 0 (-x )/(x+1) < 0 But somehow, I got the wrong answer. The answer is (4, 7]. But I don't know where I went wrong.

Homework Statement *Sorry I could not get the math symbols to work properly so I did it by hand. I hope this isn't too much trouble. Prove: | sqrt( x ) - sqrt( y ) | <= | sqrt ( x - y ) | for x, y >= 0 Hint: Treat the cases x >= y and x <= y separately. I am new to proofs and we can't use...

Why does |e^i| = 1 ?

Excuse me for my english; Decide for all the x so this works out; ((2x-7)/(x3+3))<(9/x)<=x²-5x+9 where "<=" is the same as "and =". Having some troubles getting the right values between (9/x)<=x²-5x+9, but otherwise it's fine.. hope you can help me!

I solved this absolute value equation and I am confuse about the answer given in the book for this question, the answer in the book is x > = 0 or x = -2/3 please tell me how can I get this answer from the following solution. Please tell the method which should be true for all such type of...

Suppose we have this absolute value question | x-3 | = 3 – x If we solve this question we break it as X - 3 = 3 – x or -(x - 3) = 3 - x Now if we solve it we come to know that the part on right is true for all real numbers And the part on the left is true for only 3 I also have read that...

Homework Statement Solve the inequality and sketch the graph of the solution on the real number line. Homework Equations |x - a|< or equal to b, b > 0 Let us imagine that the ">" and "<" signs also include "equal to" except for the condition, b > 0, in order to solve this...

Homework Statement I have E(a) = 0, E(b) = x but E(|a+b|)=?? where E is the expectations operator and x is a known constant which is greater than zero. Homework Equations Any one know how I would go about determining E(|a+b|)?

I've been thinking about getting a tattoo. I was considering getting the infinity symbol inside of an absolute value. Or the absolute value of infinity. Whichever you prefer. How mathematically correct is that? The absolute value of infinity simplified is infinity is it not? Will I completely...

Homework Statement If a,b are real numbers and b does not equal zero show that |a|=sqrt(a^2) and |a/b|=|a|/|b|. Homework Equations I know that |ab|=|a||b| and a^2 = |a|^2 The Attempt at a Solution Attempt at showing that |a|=sqrt(a^2): |a|=sqrt(a^2) |a|^2=(sqrt(a^2))^2...

Hi, I came across a book which looks at a problem like \lim_{x \to 0}\frac{1}{x} So you approach from 0-, and get -∞, approach from 0+, get ∞ Then it would write the answer as \lim_{x \to 0}\frac{1}{x} = \left| \infty \right| It looks bizarre to me. How do you parse this? Is...

Homework Statement how do I solve this? I am confused... |2x - 1| = x^2 Homework Equations The Attempt at a Solution when i tried it I ended up with a solution set of (1,-1). But the official answer is quite different so I am confused!

Homework Statement If f(x) is equal to... x+9 if x<-3 -2x if |x|\leq 3 -6 if x > 32. The attempt at a solution The first and third "segments" of when the function is defined as being x+9 and -6 are pretty straightforward to me, however I am unaware of the significance of the placement of the...

Homework Statement Find the CDF of |X|, given that X is a random variable, uniformly distributed over (-1,3). Is |X| uniformly distributed? If yes, over what interval?Homework Equations The Attempt at a Solution I found so far that: Setting Y=|X| Then: Y \in (1,3) F_{Y}(y)=P\left\{Y\leq...

Homework Statement How do split \int^1_{-1}\left| \frac{1}{2}+xt\right|dt Homework Equations The Attempt at a Solution \int_{-1}^0 -\frac{1}{2}-xt dt+\int_0^1 \frac{1}{2}+xt dt Im not sure if this is right, and if it is... i still don't understand how to split the absolute...

How we can integrate this (without integration limits) sqrt (|x|)

This is a physics problem, but I only need help with the calculus portion of it. I was having trouble figuring out how to split the integral to properly integrate. Homework Statement Homework Equations \int\stackrel{\infty}{-\infty}(x/x_0)e-2|x|/x_0dx where x_o is a constant...

Hi everyone; I've got this question concerning absolute value, although I understand the concept of absolute value, I can't quite understand why option B is bigger than option A. I would really appreciate some explanation on the following question: I am trying to post it in Latex, but in case...

Homework Statement I need to find where these intersect: y = |x| 3y - x = 8 Homework Equations The Attempt at a Solution I equate them: |x| = (1/3)x + (8/3) |x| - (1/3)x - (8/3) = 0 |3x| - x - 8 = 0 |2x| - 8 = 0 |x| = 4 Is that right? How do I get the other solution?

Homework Statement Hi all I have f(x)=|x|. This I write as f(x) = -x for x<0 f(x) = x for x>0 f(x) = 0 for x=0 If I want to show that f(x) is not differentiable at x=0, then is it enough to show that f'(x) = -1 for x<0 f'(x) = 1 for x>0 and from this conclude that it is...

Homework Statement Given: |A|+A+B=15 and A+|B|-B=13. What is A+B equal to? Give all possibilities. Homework Equations The Attempt at a Solution I solve for both absolute variables. So, A=15-A-B or A=A+B-15 and B=13-A+B or B=A-B-13 Firstly, I solve for A. A+A=15-B...

Homework Statement In Spivak's Calculus 4e, he defines absolute value as: |a|= a,\qquad a\ge 0 \qquad \text{ and } \qquad -a,\qquad a \le 0 Did he really mean to include the '\le ' and not just '<' ? I know it does not affect the answer, but I didn't think that you could...

Homework Statement Define sequence \left[ {z_n} \right]} _{n=1}^{\infty} of points in the complex plane with z_1 = 1 and z_{n+1} = (4+3i)z_n - 1. Show that |z_n| \ge 4^{n-1} for all n \ge 1.Homework Equations The Attempt at a Solution The base case of induction is true, since |z_1| \ge 4^{1-1}...

Homework Statement I need to simplify the expression below. The absolute value is throwing me off \left[\left|(\alpha + k)^{2}e^{-2i \alpha a} - (\alpha - k)^{2}e^{2i \alpha a}\right|\right]^{2} Homework Equations I know \left|e^{ix}\right| = 1 The Attempt at a Solution I...

Homework Statement 1) x^5 > x^2 2) 7| x + 2 | + 5 > 4 3) 3 - | 2x + 4 | <= 1 Homework Equations The Attempt at a Solution 1) x5 - x2 > 0 x2(x3 - 1) > 0 x2(x - 1)(x2 + x + 1) > 0 Im not too sure what to do next. I can't factor it any further, at least I don't think so. Which...

Homework Statement Find f'(x), if f(x) = [x^2 * (3x + 2)^(1/3)] / [(2x - 3)3] Where the absolute value symbol surrounds the entire function. Homework Equations N/AThe Attempt at a Solution My attempts don't account for the absolute value of the function. Otherwise, I can still take the...

First order linear ODE-integrating factor with absolute value?! Homework Statement Solve the ODE y' + (3/t) y = t3. 2. Homework Equations /concepts 1st order linear ODE The Attempt at a Solution Integrating factor =exp ∫(3/t)dt =exp (3ln|t| + k) =exp (ln|t|3) (take constant of...

I'm looking at this problem below: http://apthtml.com/images/deriv.png The first part I understand - a derivative of some vectors, not a big deal - but the second part is where I'm confused. I can't even come up with a name for it. First I thought magnitude, but I don't really see how...

[b]1. Solve: l2x^2+7x-15l<10 [b]3. I split it up into two cases and got: 2x^2+7x-25<0 and 2x^2+7x-5>0 With the quadratic formula I got: x= [-7+/- (249)^(1/2)]/4 and x= [-7+/- (89)^(1/2)]/4 These clearly are the answers, but I am confused about the inequality from this...

Absolute value of acceleration Help! Homework Statement I am getting a value of -1.94 m/s^2 for my acceleraton. An it wants to know the absolute value of acceleration what do I put down. It also state that the plus or minus is just to indicate direction. But the way the problems is computed...

Here's the thing. I have 4,7 nF capacitor and AC: 1 kHz < f < 10 MHz. I measure real and imaginary part of capacitance C*=C'+iC" (C'=C'(f) and C"=C"(f)). I did 2 measurements - in first capacitor is directly attached to measuring device, in second I use 1 m coaxial cables to attach it. I...

Quadratic equation and absolute value... Consider equation |x2-2x-3|=m, m belongs to R If the given equation has no solution then find the interval in which the m lies. 2. Homework Equations -Given in question 3. Since this equation is in modulus there would be two equations...

Homework Statement i just want to know one value that i can't find anywhere, and would love some help Homework Equations \lim_{x\rightarrow\ -\infty}|x|} The Attempt at a Solution thanks

Homework Statement \int_{-3}^{3}|t|e^{-jwt}dt The Attempt at a Solution I am not sure if I need to break this into two regions due to the abs value...

Homework Statement |1/(x-1)|<1 The Attempt at a Solution is that the same as this -1<1/(x-1)<1 can i do each side by it self then take the values at which they intersect so i subtracted the 1 then got (-x+2)/(x-1) then made a sign chart with 2 and 1 on it then took the less than...

Homework Statement Find \frac{d}{dx} \sin^{-1}(\sin x) Homework Equations The Attempt at a Solution Now, I know that the above expression simplifies directly to \frac{d}{dx} x = 1, but I attempted it the long way. Here it is: \frac{d}{dx} \sin^{-1}(\sin x) = \frac{\cos...

Homework Statement I previously left some absolute value questions which contained a few simple equations and equalities. i have a further question when it comes to slightly more complicated Absolute statements. Sketch the graph of y = 2|x-1| - 3|x+1| + 3x + 1 Homework Equations...

I'm stuck trying to prove a step inside a lemma from Serre; given is 0<a<b 0<x To prove: |\int_{a}^{b}e^{-tx}e^{-tiy}dt|\leq\int_{a}^{b}e^{-tx}dt I've tried using Cauchy-Schwartz for integrals, but this step is too big (using Mathematica, it lead to a contradiction); something...

When is it true that is |a|=|b|, then either a=b or a=b*, where a and b are complex numbers and b* is the complex conjugate of b?

Homework Statement Integrate using Cauchy Formula or Cauchy Theorem: I=\oint_{|z+1|=2}\frac{z^2}{4-z^2} dz (From Complex Variables, Stephen Fisher (2nd Edition), Exercise 2.3.3) Homework Equations \frac{1}{2\pi i}\oint_{\gamma} \frac{f(s)}{s-z} ds= \left\{ \begin{array}{lr}f(z) & : z \in...

Hi all, I'm wondering about this question I can prove that if lim_{n->inf} (a) = L then lim_{n->inf}abs(a) = abs(L) however.. is the converse true? thx

In order to get an integral I need to find the difference between two functions, but I'm not sure how to deal with the absolute value... f(x) = \left|x-1-1\right| g(x) = x^2 + 2x g(x) - f(x) = (\left|x-1\right|-1) - (x^2 + 2x) =... I don't know if I can simplify it anymore... can I...

when i am exploring a function eg. f(x)=|2x-6| can i treat it as two separate function all the way through, one to the left of x=3 and one to the right, and only at the very end, when i draw the graph connect them, ie draw a graph according to all the values i found from each side? will this...

Let z be the complex number: x+iy. Then |z|^2=x^2+y^2 according to my book. But according to the general definition of absolute value, |a|=(a^2)^.5. So letting z=a=x+iy. |z|^2=z^2=x^2+2ixy-y^2 This is not equal to x^2+y^2. I'm confused.

Homework Statement Find: Lim | x2+x-12 |-8 / (x-4) x --> 4 Homework Equations The Attempt at a Solution My answer is 9. It it right ? or there is not a limit for F(x) when x --> 4