What is Absolute values: Definition and 77 Discussions

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and |x| = −x if x is negative (in which case −x is positive), and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.
Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.

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  1. X

    Trigonometric sum-difference formula for absolute values

    sin|x + y| = ? cos|x + y| = ? Is there any formula for these?
  2. N

    Absolute values in standard integrals

    In a lot of compilations of standard integrals (my Calculus book does this, Wikipedia does this), a lot of the integrals of trigonometric functions have an absolute value in their solution which seems out of place to me. For example, take the integral \int dx \cot{x}. My Calculus book says...
  3. H

    What is the domain and asymptotes for f(x) = |x³ + x²|/(x² - 1)?

    Hi! I've got a problem that's got me a bit.. well, in the end I guess the proper word is sceptic, because it feels a bit like I've made the answer up, which is why I'm taking it up here at all. Anyway: Homework Statement Determine the domain for f(x) and the asymptotes to the curve y=f(x) for...
  4. H

    Solve Absolute Values: z∈C |z - 1| = 5, |z - 4| = 4, |4 - z2| = z

    Homework Statement So I've got two problems I'm struggling a bit with. One of them I've solved (I think), but I'm definitely not sure. The other one is bugging me a bit. Anyway: i] Determine all z∈C so that |z - 1| = 5 and |z - 4| = 4 ii] Determine all z∈C so that |4 - z2| = z...
  5. P

    Spivak Calculus chapter 1: absolute values?

    Homework Statement http://img3.imageshack.us/i/0902091724.jpg/ http://img3.imageshack.us/i/0902091724.jpg/Homework Equations The Attempt at a Solution My problem is that I don't even know where to start on this! My first problem is always forgetting what I can and can't use, because we can...
  6. D

    What is the limit of |x+1| as x approaches -1?

    Homework Statement Evaluate. lim |x+1| x-> -1 Homework Equations The Attempt at a Solution Not too sure what |x+1| means. I think it has something to do with an absolute value... would the answer be 2 then?
  7. P

    How Do Absolute Values Affect Solving Function Equations?

    Homework Statement I do not see how the two equations in each example are related, what should I do with them? (the l's are absolute value brackets): a) Let g(x) = 3x - 3 + l x+5 l. Find all values of a which satisfy the equation: g(a) = 2a +8 b) Let h(x) = l x l - 3x...
  8. U

    Calculating integrals of area between two functions, involving absolute values

    Hi all, I'm currently preparing for pre-tertiary mathematics, studying from Apostol's "One-Variable Calculus". I have just begun to work on the theory of integration of trigonometric functions, but I found that with the last set of exercises (on finding area between two functions, over some...
  9. S

    Trying to derive this but has multiple absolute values

    Homework Statement Find the Local and absolute extrema of f(x) on the interval [-1,2] and give a sketch of the graph if: f(x) = [ 1 / (1 + |x|) ] + [ 1 / (1 + |x - 1|) ] I am confused about the absolute value parts. I know they're the versions inside the absolute value signs when...
  10. R

    Divisor proof with absolute values

    Homework Statement I reduced a much harder problem to the following: Prove that if abs(a-b) is divisible by k, and if abs(b-c) is divisible by k, then abs(a-c) is divisible by k. Homework Equations none really. The Attempt at a Solution I tried setting abs(a-b)/k = n and abs(b-c)/k = m...
  11. M

    Solving quadratic inequalities and absolute values

    Homework Statement lxl <2 lx+2l The question is asking to solve this Homework Equations The Attempt at a Solution Ive tried bringint the 2 over which leads me to l-x-4l over lx +2l < 0 but then the absolute value confuses the heck out of me on where to go...
  12. H

    Definite integrals of absolute values

    Homework Statement \int|x^{2}+x-2|dx from -2 to 2 Homework Equations The integral of f(x) from a to b = F(b) - F(a) |x| = { x if x >= 0; -x if x < 0 --- Ok, I don't know how to do the definite integrals of absolute values.. was never shown an example of it in class, but I kind of...
  13. F

    Derivatives of absolute values

    Homework Statement Where is the function f(x) = |x| differentiable? Homework Equations [f(x+h) - f(x)] / h The Attempt at a Solution I know that the graph of f(x)=|x| shows a corner at the origin from which 2 lines project at opposite slopes, as in they are symmetric about the...
  14. R

    Absolute Values and Continuous Functions

    Homework Statement We recently proved that if a function, f, is continuous, it's absolute value |f| is also continuous. I know, intuitively, that the reverse is not true, but I'm unable to come up with an example showing that, |f| is continuous, b f is not. Any examples or suggestions would...
  15. Z

    Trig integrating with absolute values:

    Homework Statement \int_0 ^\pi \sqrt{1-\sin^2 x} dx Homework Equations 1 - \sin^2 x = \cos^2 x The Attempt at a Solution I don't know how to treat this since cos changes sign half way across the integral. I know the answer should be 2 but I keep getting 0 every which way I try.
  16. A

    Finding limits with absolute values

    I need help finding limits. I know it's pretty simple most of the time... I know that for example if the lim x--> 3 of x-3, you just plug 3 for x... what do I do if it's the absolute value of x-3? I know you guys like to see that I've tried to solve the problem, but there's not much I can...
  17. R

    A little clarification on absolute values

    Hello again. I have a (stupid, but I'm not real sure about the answer-type) question. I'm trying to prove that the second order ODE of the simple pendulum y''=-(g/l)sin y is Lipschitz (using norm 1). After doing some evaluating, I came up with |u'-v'| + |\frac{g}{l}||\sin u - \sin v| All I'm...
  18. N

    Stuck on an inequality with absolute values

    Hi, I'm stuck on the following problem: |(4/x)| > 5 I split it up into two cases, case 1 is x > 0, case 2 is x < 0 Case 1: Case 2: 4/x > 5 4/x < -5 4 > 5x 4 < -5x 5x < 4 -5x > 4 x < 4/5...
  19. D

    Finding the limit of a function with absolute values.

    I need a little help and reassurance here. The question is as follows, Find the following limit, if it exists. \lim_{x \rightarrow 1} \frac{x ^ 2 + |x -1| - 1}{|x-1|} Here is what I did, first I did the two one-sided limits, as \lim_{x \rightarrow 1^+} and as \lim_{x \rightarrow 1^-}. (the...
  20. J

    Absolute Values: Is it a Mistake or Something I Don't Know?

    An example in my textbook gives \vert \frac{5-x}{5x} \vert \Leftrightarrow \frac {1}{5} (\frac{1}{\vert x \vert}) (\vert x-5 \vert) Is there something I don't know about absolute values that allows \vert 5-x \vert to become \vert x-5 \vert or is this a mistake in the text?
  21. Y

    Explaining the Definition of Absolute Value

    so if |x|=(x,if x>=0, and -x, if x<0) then what would be like |x-7| be equal too and how do you do this i do not understand why |x|equals (x,if x>=0, and -x, if x<0) could you explain it to me?
  22. J

    How Can I Simplify and Shift the Graph of Absolute Values?

    I'm supposed to sketch this graph \vert x \vert + \vert y \vert = 1 + \vert xy \vert I think the purpose of the exercise is to simplify this into something that resembles a typical function and be able to shift the graph over so that it looks normal. I'm having troulbe getting the y's...
  23. JasonRox

    Understanding Absolute Values: Tips and Tricks to Mastering the Concept

    This is easy, but for some reason I can't grasp the idea. |x-1|+|x-2|>1 I know it means that the distance between x and 2, and x and 1 is larger than 1. It isn't school related, and I did search online, but they are simple ones like... |x-1|>1 Can anyone help me? Thanks.
  24. vincentm

    Absolute Values: N00b Lesson for Beginners

    Can someone give me a n00b lesson in absolute values, i though i remembered, but i don't. I got stuck on a -|-8| :blushing:
  25. S

    How do you deal with absolute values in your Integrals?

    I have to solve the integral: \int^1_{-1} e^{-| |x| - \frac{1}{4} |} dx but I have no idea what to do with the absolute value signs. Can someone help me? :confused:
  26. G

    Solving inequality with absolute values |3x-2|<=x+1

    1) │3x-2│<= x+1 ; x>=-1 Case1: 3x-2>=0 x>= 2/3 3x-2<=x+1 x<=3/2 what is case 2? 2) │2-3x│ < 3x-4 3) │x-3│=x-2 How do u solve these?
  27. A

    Graphing calculator Absolute values? HOW?

    Does anyone know how to put absolute values in the t1-83 graphing calculator? I need to graph absolute value of x, the absolute value of x +2, and the absolute value of x-3
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