What is Absolute: Definition and 1000 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. J

    How Do You Calculate Absolute Pressure at a Depth Using Bubble Size Changes?

    Problem: An air bubble originating froman under water diver has a radius of 5 mm at some depth h. When the bubble reaches the surface of the water, it has a radius of 7.4 mm. Assuming the temperature of the air in the bubble remains constant, determine the abso- lute pressure at this...
  2. S

    How to Split Absolute Value in an Integral

    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...
  3. C

    Absolute relative approximate error

    I'm a bit confused, i have a question, it asks me to find ''the absolute relative approximate error'' at the end of each iteration. What's the formula of ''the absolute relative approximate error''?
  4. T

    Solve Absolute Parabola: Sketch |x^2 - 2x - 3| Graph

    Homework Statement Sketch the graph of |x^2 - 2x - 3| Homework Equations None The Attempt at a Solution |x^2 - 2x - 3| = { x^2 - 2x + 3 x^2 - 2x - 3 >= 0 x >= 3 OR x >= -1 {-x^2 + 2x + 3 x^2 - 2x - 3 < 0 x < 3 OR x < -1 if x < -1 then y = -x^2 + 2x + 3 if -1...
  5. U

    Absolute begginer's question (direction of current flow)

    So I've been trying to wrap my head around the concept of the direction of current flow. I thought a voltage divider would be a good place to start. One website I've visited told me that the following image is a voltage divider. Both R1 and R2 will work together to affect the voltage of...
  6. J

    Applied problem using absolute extrema

    Hi, I have a problem solving this question, I don't know if I am on the correct track for solving this. Suppose that the sum of the surfaces of a sphere and a cube is constant. Show that the sum of their volumes is smallest when the diameter of the sphere is equal to the length of an edge of the...
  7. H

    Absolute Maxwellian acceleration?

    This recent thread: https://www.physicsforums.com/showthread.php?t=386121" leads me to the following thought experiment: Your spaceship flies by another spaceship which appears to be highly electrically charged. From measurement of E and B fields on board your craft, you conclude that...
  8. Q

    Speed of sound in sodium at absolute zero?

    I don't need help with a numerical solution here - mostly a concept check. I've been asked to calculate the speed of sound in metallic sodium at T = 0 K using Fermi-Dirac statistics. After doing so, I get a speed of 14.5 meters per second, which is, well, really slow. I would have...
  9. J

    Absolute Extrema F(x,y) 0<x<π, 0<y<π

    Homework Statement F(x,y)= sin(x)sin(y)sin(x+y) over the square 0< x< pi and 0< y< pi(The values for x and y should be from 0 to pi INCLUSIVE) Homework Equations The Attempt at a Solution partial derivative in terms of x = siny[cosxsin(x+y)+sinxcos(x+y)] you get y=0, pi because siny =0, but...
  10. J

    Multivariable Calc Absolute Extrema Problem

    Homework Statement F(x,y)= sin(x)sin(y)sin(x+y) over the square 0\underline{}<x\underline{}<pi and 0\underline{}<y\underline{}<pi (The values for x and y should be from 0 to pi INCLUSIVE) Homework Equations The Attempt at a Solution I know I need to do the partial derivatives...
  11. moe darklight

    Is my proof for Absolute convergence => Convergence right?

    Is my proof for "Absolute convergence => Convergence" right? I had to prove it for my calc test today; my proof looks different than the one my prof posted as the answer; it's also way shorter. He used the one from the book but I didn't memorize it so I used this. Is it right? Homework...
  12. J

    Find absolute extrma of sin(cos(x))

    Homework Statement A simple question; find the absolute extrema of f(x)=sin(cos(x)) on the interval [0,2pi]. Homework Equations The chain rule The Attempt at a Solution Assuming that I am correct about the derivative being -cos(cos(x))sin(x), how do you solve -cos(cos(x))sin(x)=0
  13. J

    Finding Absolute Extrema: Solving for Critical Points in Rational Functions

    Homework Statement (16x)/(x^2+4) for -5 (less than OR equal to) x (less than OR equal to) 5 Homework Equations Set the derivative of the equation equal to 0, solve for x to find the critical points, then plug and check for validity. The Attempt at a Solution I used product rule for...
  14. A

    Integrate absolute value

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

    How do u convert relative angle to absolute angles?

    ie: in the figure theta 3 i got i want theta 2 what formula would i use
  16. C

    Is spacetime an absolute reference frame?

    STUPID QUESTION ALERT! Is spacetime an absolute reference frame?
  17. M

    Proving Non-Continuity at (0,0) for f(x,y) = |xy|

    Homework Statement Let f(x, y) = |xy|. I want to prove that f is not continuous at (0,0). The Attempt at a Solution To prove that f is not continuous at (0,0) I think I need to show that \lim_{(x, y) \to (0, 0)}|xy| \neq 0 I'm a little confused about the |absolute value|...
  18. K

    Splitting an integral with an absolute value

    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...
  19. C

    Question related to Absolute Value

    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...
  20. X

    Trigonometric sum-difference formula for absolute values

    sin|x + y| = ? cos|x + y| = ? Is there any formula for these?
  21. J

    Does absolute makes a difference in area

    Homework Statement y = 2 − x^2, y = |x| sketch and find the area of the region determined by the intersections of the curves Homework Equations regular f - g of integral The Attempt at a Solution The absolute value puzzles me. How would it work then? I mean we know how each...
  22. C

    Absolute color - magnitude diagram

    Hello all, I am finding a distance to a cluster via Main Sequence fitting, and I don't know where to find an absolute color - magnitude diagram ( B-V, and V ). I can be from any star cluster, or sky region, as long as the magnitudes are absolute. I need the data tables, not just a pretty...
  23. M

    Absolute & conditional convergence

    Homework Statement Determine whether the series converges absolutely, conditionally, or not at all. a) \Sigma (-1)nn4/(x3 + 1) b) \Sigma sin(x)/x2 Homework Equations The Attempt at a Solution a) positive series is n4/n3+1 .. do i do comparison test ?? b) |sin(x)|/x2...
  24. D

    Find Absolute Max/Min of f(x,y)=xy^2 w/ Domain x^2+y^2≤4

    Can anyone tell me the general procedure in doing the following procedure? f(x,y)=xy^2 with domain x^2+y^2\leq4 Find it's absolute max & absolute min. Okay, here is my thought procedure, tell me what I can fix. So I would basically say, find the partial derivatives with respect to x and y...
  25. D

    What are the absolute min and max of f(x,y)=xy^2 over a specific domain?

    Find the absolute min & absolute max of f(x,y)=xy^2 with domain x^2+y^2\leq4 Please help
  26. H

    Ideal gas and absolute zero

    Homework Statement Calculate your experimental value of absolute zero , how does your experimental value compare to the theoretical value -273C? Homework Equations T_abs=(S1*T2-S2*T1)/(S1-S2) The Attempt at a Solution This is all part of a lab. I'm not asking people to do any...
  27. 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...
  28. A

    Absolute Time vs Relative Time

    What does QM have to say on the ontology of time? Is time absolute or relative? What does quantum entanglement have to say on the subject?
  29. Z

    Factoring something with absolute value

    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?
  30. D

    Question on finding absolute pressure?

    Hey, here's the question: "If a gauge reads -295mmHg where athmospheric pressure is 101.7 kn/m^2 and the vapor pressure is 2.8 kN/m^2, what is the absolute pressure?" I converted the gauge pressure to 39.36 kN/m^2 but where do i go from here? I know the equation is p_gauge= p_absolute -...
  31. D

    Physics question on absolute pressure?

    Hey, here's the question: "If a gauge reads -295mmHg where athmospheric pressure is 101.7 kn/m^2 and the vapor pressure is 2.8 kN/m^2, what is the absolute pressure?" I converted the gauge pressure to 39.36 kN/m^2 but where do i go from here? I know the equation is p_gauge= p_absolute -...
  32. G

    Does a Black Hole Represent a State of Absolute Rest in the Universe?

    Hello... If time stops at the event horizon of a black hole..which means there is no motion happening or can be observed..does that not mean that the centre of a black hole is a place of absolute rest? Could such a place of ab/rest 'move' thru the cosmos (basically a black hole which is a...
  33. J

    Relative extrema of absolute functions

    Find the relative extrema of f(x)=|3x-x^2|. Normally you solve f'(x)=0 to find the critical points, in that case we have 3-2x=0 => x=3/2. However there are two other relative extrema that I cannot find by calculus as the absolute nature of f(x) has confused me. Indeed doing a sign analysis on...
  34. M

    Absolute Entropy (Statistical)

    I was looking at a derivation of entropy expressed as an absolute probability: S = -k. SUM P.lnP (What is the name of this by the way?) In the derivation, it makes the following statements which I really just don't get! U = SUM E.P so therefore dU = SUM E.dP - SUM P.dE Where does...
  35. N

    Frame dragging and absolute rotation

    I'm trying to wrap my head around how rotational frame dragging affects the centrifugal force of a massive, rotating body and was hoping someone could explain this concept to me better. If I am confused on any of the points below please let me know. It is my understanding that there is no...
  36. N

    Absolute value and differentiability

    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...
  37. J

    Absolute Potential: What is Meant?

    What is meant when the potential difference of a point in space is quoted? (my book calls it absolute potential). What "difference" is being referred to (only one point is being referenced)?
  38. N

    No Absolute Stillness: Questions from New Forum Member Nick

    Hi everyone, I am new to this forum - happy to meet you! :-) Background to my questions: According to quantum physics, there is no "absolute stillness" (but always some "quantum noise"). This seems to be one of the implications of Heisenberg's uncertainty principle (because if there was...
  39. E

    Absolute zero and hot in respect to time dilation

    I was thinking, if time passage varies with speed would the speed of atoms random movement (temperature) affect time? For example, if the universe is expanding, as some predict, it will eventually reach a state where everything will reach very near to absolute zero, or maybe absolute zero. If it...
  40. R

    Absolute vacuum between atoms?

    Isn't the distance between two atoms where nothing exists, no atoms or subatomic particles, absolute vacuum? a place where nothing exists?? I am not too educated in such physics, so please do explain what you say
  41. G

    Organic matter in absolute zero?

    For example, what happens if you put an apple in space? Or what happens when animals (or people) are frozen to very low temperatures?
  42. S

    Absolute convergence: ratio/root test n/n^n

    Homework Statement Doing some problems from textbook, I need to determine whether the series is absolutely convergent, conditionally convergent, or divergent. n!/n^n I plugged it into WA, and it says the series doesn't converge, but I'm not sure how to figure it out. Homework...
  43. K

    The impossibility of absolute rigidity during collisions

    Let's say we have two perfectly rigid spheres. One is at rest and the other is moving toward it with some differentiable velocity. When they collide, the first sphere will start moving with infinitesimal velocity and the second will reduce its speed by an infinitesimal amount. But since the...
  44. F

    Solving two absolute value variables.

    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...
  45. Saladsamurai

    Spivak Error? Definition: Absolute Value

    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...
  46. S

    Calc Integral: |sinx-cos2x| from 0 to \pi/2

    \int^{\pi/2}_{0}|sinx-cos2x| dx Hi guys i can't seem to get the correct answer for this. What i did was draw the graph of sinx and cos2x and for 0 to \pi/6 i use cos2x-sinx since cos2x is higher. From \pi/6 to \pi/2 i use sinx-cos2x. However i am not able to get the same answer as my book can...
  47. I

    Absolute Min/Max, Bounded region

    Homework Statement Find the abs min/max values of the function f(x,y) = e1-2x2-y2 on the closed and bounded region x2 + y2 <= 1 The Attempt at a Solution First I have to find the critical points Dfx = (-4x)e1-2x2-y2 Dfy = (-2y)e1-2x2-y2 Clearly e1-2x2-y2 cannot equal 0...
  48. H

    Absolute Max/Min of f on [0,8]

    Homework Statement Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x/(x^2 + 25) [0, 8] Homework Equations taking derivatives are necessary The Attempt at a Solution f(x)= \frac{x}{x^2+25} f'(x)= \frac{(x^2+25)-x(2x)}{(x^2+25)^2}...
  49. M

    Absolute Min of y=x Sqr.Root (3-x) in Domain (-infinity, 3]

    fuction is y=x sqr.root (3-x) Domain (-infinity, 3] i got my critical numbers to be x= 2, 3 Now i know the absolute max is x=2. but for the absolute min, would it be at x=3? or none since the function continues to go to negative infinity as x approaches negative infinity?
  50. H

    Find Absolute Max/Min for Function with Domain.

    [b]1. Find absolute max/min for the given function with the specified domain. f(x,y)= x^2-xy+y^2 on the circular disk x^2+y^2 less/equal 4, use parametrization when checking boundary. [b]2. f(x,y)= x^2-xy+y^2 x^2+y^2 less/equal 4 [b]3. The only thing I...
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