Absolute Definition and 1000 Threads

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. 9

    Absolute value and piecewise functions

    Homework Statement Find if continuous and differentiable. I am having problems with the differentiable part. Homework Equations f(x) = x² + 3, |x| ≤ 1 f(x) = |x| + 3, |x| > 1 The Attempt at a Solution (1)^2 + 3 = 4 |1| + 3 = 4 ∴ It is continuous Now, rewriting it, you...
  2. M

    Definite Integral with Absolute Value.

    The problem is ∫x^2 - 3x - 5 with the lower limit being -4 and the upper limit 7. I broke the integrals into three parts from [-4, -1.1926], [-1.1926, 4.1926], [4.1926, 7] I did the integral and got (x^3)/3 - (3/2)x^2 - 5x I subbed in the lower and upper limits and got 32.861 for [-4...
  3. E

    Question about absolute value limits?

    When do you check the limit from the right and left of a limit with an absolute value in the numerator or denominator? For example, why do you check the limit from both sides of: Lim x -> 3/2 (2x^2-3x)/absolute value(2x-3) But only the left side of: limit as x approaches -2...
  4. J

    How to Calculate Absolute Error Correctly?

    calculate the absolute error of a) 0.0342 m +- 5% b) 0.0342 m +- 0.5% Did I do these correctly? a) 0.342*.05=1.71 so round it to 2 m b) .0342*.005=1.71 (there was a 10^something after these numbers on the calculator) so round it up to 2 meters again Did I do those correctly?
  5. S

    Prove that the absolute value of a dot product is less than or equal t

    Homework Statement That is prove that |a•c|≤|a||c| for any vector a=<a1,a2,a3> & c=<c1,c2,c3> Homework Equations The Attempt at a Solution I really don't have much of an attempt at the solution. I am not sure where to start. I can kind of justify it in my mind by saying the...
  6. ckirmser

    How to Determine Absolute Magnitude

    Hello, all. I'm trying to find an equation to determine a star's absolute magnitude in order to populate a table of stellar characteristics. Unfortunately, every formula I've run across requires a star's apparent magnitude and that requires knowing how far the star is from the observer...
  7. M

    Is Wolfram the Key to Solving Tricky Equations on the Go?

    Solve |x^2-5|=4|x|. I tried to rewrite it as: (sqrt(x^2-5))^2=4*(sqrt(x))^2 Is this the right way to solve the equation?
  8. N

    The fundamental forces and elementary particles at absolute zero

    We all know that there four fundamental forces in nature, viz. The gravitational force The electromagnetic force The strong nuclear force The weak nuclear force Now also we know that temperature of any system is the average kinetic energy possessed by the particles of the system Now...
  9. F

    MHB Proving Absolute Convergence of a Real-Valued Function on a Sigma Algebra

    Let R be a sigma algebra and let $f$ be a real value function on R such that for a sequence ($A_{n}$) of disjoint members of R, we have that the sum of $f$($A_{n}$) over all n is equal to the image of the countable union under $f$. Prove that the sum of $f$($A_{n}$) is in fact absolutely...
  10. K

    Absolute pressure at the bottom of a container

    Homework Statement A container is filled to a depth of 20.0 cm with water. On top of the water floats a 29.0-cm-thick layer of oil with specific gravity 0.800. What is the absolute pressure at the bottom of the container? (Answer in Pa) Homework Equations P= ρgh+ P(atmospheric) The...
  11. P

    Absolute value in separable ODEs?

    Suppose I have a variable separable ODE, e.g., \frac{dy}{dx} = 3y. We all know that the solution is y=Ae^{3x} where A is a constant. My question is as follows. To actually find this solution we rearrange the equation and integrate to get \int \frac{dy}{y} = 3 \int dx, which gives \ln...
  12. M

    Absolute Extrema: Find f(x,y) over x^2 & y=4

    Homework Statement Find absolute extrema of the function over the region R. f(x,y) = 3x2 +2y2 -4y, R: the region in the xy plane bounded by the graphs of y=x^2 and y=4Homework Equations second partial derivative test d=fxxfyy-fxy2The Attempt at a Solution This is my practice test for the final...
  13. M

    Does the Derivative of the Integral of Tan(x) Consider Cos(x) Sign Changes?

    ∫tan(x) dx = -ln lcos(x)l + C = f(x) So is f'(x) = -sin(x)/lcos(x)l ? When taking the derivative, do we only consider f'(x) to only exist on the intervals where cos(x) > 0 instead?
  14. T

    Finding the CDF from a PDF with absolute value function

    Homework Statement Find the CDF of f(x) = |\frac{x}{4}| if -2<x<2 \\ 0 otherwise Homework Equations The Attempt at a Solution I have to integrate the pdf and to do so, I have to split it into two parts \int_{-x}^{0}\frac{-t}{4}dt + \int_{0}{x}\frac{t}{4}dt integrating I get \frac{x^2}{8} +...
  15. S

    Absolute continuity, function of partition bound

    Given [a,b] a bounded interval, and f \in L^{p} ([a,b]) 1 < p < \infty, we define: F(x) = \displaystyle \int_{a}^{x} f(t) dt, x \in [a,b] Prove that exists K \in R such that for every partition: a_{0} = x_{0} < x_{1} < ... < x_{n} = b : \displaystyle \sum_{i=0}^{n-1} \frac{| F(x_{i+1}) -...
  16. P

    Finding inverse when function conatains absolute value

    Homework Statement Given the function f(x) = (abs(x))*x +6, find f^-1(x) Homework Equations The Attempt at a Solution for x≥ 0, f(x) = x^2 + 6 y=x^2 +6 x = √(y-6) for y≥6 → f^-1(x) = √(x-6) for x≥6 for x< 0, f(x) = -x^2 + 6 y= -x^2 +6 x = √(6-y) for y<6 → f^-1(x) = √(6-x) for x<6 But...
  17. J

    Inequality integral absolute value derivative

    Here's a claim: Assume that a function f:[a,b]\to\mathbb{R} is differentiable at all points in its domain. Then the inequality |f(b) - f(a)| \leq \int\limits_{[a,b]}|f'(x)|dm(x) holds. The integral is the Lebesgue integral. Looks simple, but I don't know if this is true. There exists...
  18. A

    MHB Find Min/Max of f: 2cos(x)+sin(2x) & x^2+16/x

    4)Find the absolute minimum and absolute maximum values of f on the given interval. a) f(x) = 2cos (x) + sin (2x) on [0, π/2] b) f(x) = x^2 +16/x on [1, 3] Thanks again in advance!
  19. Q

    Absolute Extrema on Open Intervals

    Homework Statement Problem 2: Find the absolute extreme values of f(x) on the interval (1, infinity). Homework Equations The Attempt at a Solution It seems as if this is an indiscretion by the teacher. Absolute extrema don't occur on open intervals except in the case of (-∞,∞) such as in...
  20. V

    MHB Inequality with absolute value.

    Solve 2x - |x+1| < 4.
  21. C

    Inverse of absolute value function

    Homework Statement Y=abs -4(x+3) +1 Note: the 1 is outside the absolute value Homework Equations Switch y and x The Attempt at a Solution So you subtract the 1 to bring it to the other side After that do I put: x-1= -4(y+3) And x-1= 4(y+3) And solve for y? Am I doing...
  22. L

    When does the triangle inequality hold for absolute value?

    Homework Statement abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement Homework Equations Triangle inequality? The Attempt at a Solution I have nothing :/
  23. F

    MHB Do you need absolute value around argument for log and ln?

    When I learned about derivatives I was taught to put the absolute value sign around the argument for ln and log. For example \log{|x|} and \ln{|x|} instead of log(x)ln(x). Does this make a difference? Should both brackets and the straight lines be used? When taking the derivative what is the...
  24. G

    Integration with absolute value

    Homework Statement The problem is in the context of a probability problem; however, my question in regards to a computation regarding a particular integral. All that is needed to know is that the probability density function is 1 in the range 0 < y < 1 , y-1 < x < 1 - y, and 0 otherwise. I...
  25. B

    Is the Hayflick limit an absolute limit for the human lifespan?

    Is the Hayflick limit an absolute limit for the human lifespan or is it just the average limit of the human lifespan just like there are average heights and weights? Based on the maximum number of times the cells divide which is 50 according to Hayflick's experiments, how can the maximum...
  26. A

    Double Integral of an absolute value function - Need Help

    Hi! Need help in solving this double integral: 1 1 ∫ ∫ |x-y| dydx 0 0 Thanks in anticipation. Regards, Aby.
  27. C

    Inequality absolute value help

    ## x - |x-|x|| > 2 ## how would I go about solving something like this? my initial thoughts was to consider if x >= 0 I get 2-x < 0 then x > 2 in that case then consider if x < 0 which I get -|x+x| > 2-x then 2x > 2-x then x > 2/3 but I'm having troubles deciding which one is correct, and if...
  28. F

    [Xcode] Absolute value issue in C

    Hey PF, I'm building a simple math calculator program in C for my Programming class. My problem is Xcode doesn't recognize the absolute value function (abs), even with math.h included: Any ideas on what I can do to fix this? Is there a way for me to define this on my own? Thank...
  29. A

    Why is the derivative of absolute value of x (x*x')/abs(x)

    I have no problem that I am trying to solve but simply a question about the derivative of an absolute value equation. I know that the derivative of and absolute value function is (x*x')/(abs(x)) and I understand the process of reaching this equation through the process shown here...
  30. M

    Squaring of vectors in absolute value

    Is |\vec{a}+\vec{b}|^{2} equal to the same thing as (\vec{a}+\vec{b})^{2}? And when is it equal to √(a^{2}+b^{2})? Thanks.
  31. P

    Foucault's pendulum shows absolute motion?

    In the 19th century they believed in the absolute motion and the ether, and they were searching for a scientific proof of the motion of the Earth. When Foucaults experiment was done, people still believing that the Earth was still wasfinally convinced that it moves instead. But it is well...
  32. Y

    Converting a linear optimization problem with absolute values

    Homework Statement Here is an alternative approach to handling absolute value terms as the decision variables: abs(x) is the smallest value z that satisfies x \leq z and -x \leq z. Using this,convert the following into a lp Min 2x1 + 3abs(x2) S.T x1 + x2 \geq 6 Homework Equations Here is a...
  33. karush

    MHB Creating an absolute value equation from an inequallity

    if you are given -6 \leq x \leq 14 from this how do you create an abs equation like |x-4| \leq 10 k
  34. P

    How Do You Solve Absolute Value Inequalities Involving Fractions?

    Absolute Vales with fractions HELP PLEASE :) hey everyone, Homework Statement find the solution set: l 1/x -3 l > 6 Homework Equations none The Attempt at a Solution 1/x > 9 or 1/x < -3 1 > 9x or 1 < -3x 1/9 > x or -1/3 > x this answer doesn't seem...
  35. R

    Graph of double absolute values

    Homework Statement |x| + |y| ≤ 1 What is the region in the plane that solves this inequality? Homework Equations The Attempt at a Solution I first tried graphing it by isolating the y variable |y| ≤ -|x| + 1 Then I looked at the hint we were given, which was to assume that x and y...
  36. C

    Finding Absolute Uncertainty Using Formulas

    Homework Statement Hello, I have solved the problem, but not the way the writer intended. I need help figuring out how they wanted me to do it. Here's the problem: The circumference of a sphere is found to be 0.98 m +/- 0.01 m. Calculate the volume and absolute error with five digits...
  37. paulmdrdo1

    MHB Integration with absolute value.

    $\displaystyle\int|2x-1|dx$ please tell me what is the first step to solve this.
  38. E

    An object above absolute zero radiates energy

    An object above absolute zero radiates energy. This implies that object on Earth too radiate energy(infrared?) My question is, if the Earth were not moving, we would be much slower, so would we radiate in some other wavelength of the spectrum? We are essentially traveling really fast because of...
  39. anemone

    MHB Absolute Value Function Challenge

    Solve $||||||| x^2 – x –1 |–3|–5|–7|–9| – 11|–13| = x^2 – 2x – 48$.
  40. S

    Finding flux from apparent and absolute magnitude

    How much flux reaches Earth from an unobscured star? ##m_{sun} = -26.83## and ##M_{sun} = +4.74## ##m = +6## and ##M = +4.74## Calculated distance of target star: ##d = 17.86 pc## Now, here I'm trying to find the flux of a star that has the same absolute magnitude as our sun, but has an...
  41. K

    Absolute zero and vibrating atoms

    I am trying to get a better understanding of what it means for an atom to vibrate. Let's say there is a chunk of iron in deep space that starts out with a temperature of 50 degrees celsius and is rapidly losing thermal energy. I will make the following assumptions: 1. The iron has thermal...
  42. D

    MHB Solving an absolute value equation and the defference between two quadratics

    Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 9) Solve for all X: |2x-5| + 3 = 18 My Answer: x = 10, x = -5 10) Subtract and simplify: (5x^2 - 3x + 8) - (-4x^2 - x + 10) My Answer: 9x^2 - 2x - 2
  43. W

    Why is the value of PI not absolute?

    Why is the value of PI not absolute mathematically?
  44. A

    Does absolute space explain the inertial and non inertial forces?

    The title might be confusing. Anyway while preparing for a seminar I made a statement, " Absolute space does not explain the inertial forces, since they are related to acceleration with respect to anyone of the inertial frame". Is this statement correct? Please explain with few examples, Thank you..
  45. J

    Limit of (-1)^n(2n^3)/(n^3+1) using Absolute Value Theorem

    Homework Statement Find the limit of this sequence: (-1)n(2n3)/(n3+1) Homework Equations The Attempt at a Solution At first glance I would attempt to use the absolute value theorem which gives an answer of 2 as n approaches infinite. My question is, when the theorem fails (...
  46. Darth Frodo

    Mean Absolute Percentage Error in R

    Hi all, I'm trying to calculate the M.A.P.E. using the accuracy() function in SDMtools. I have an output of 10.69. I'm not sure if this is 10.69% or 1069% as previously in a different model I had gotten an output of 0.34. If anyone is familiar with this, I would appreciate any help...
  47. J

    Algebra with absolute value. Please help me to to solve.

    I came across this algebra problem, can someone please help me solve this problem? Please show the steps as well. Much appreciated. |(x-1)| + |(y-3)| = 11 |(x- 3)| + |(y-17)| = 3 Find the nearest/possible x and y
  48. R

    Finding Absolute Min Value of OP + OQ with Slope m

    Homework Statement A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. As L varies, what is the absolute minimum value of OP + OQ? The attempt at a solution Let x and y be two points on the line. Using the slope...
  49. Fernando Revilla

    MHB Solving Absolute Value Inequalities: Steps & Link to Yahoo! Answers

    I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.
  50. 1

    Looking for a simple generalization regarding absolute values

    Hi all, I was working on a proof that essentially worked because: |x-y|+|y-z| >= |x-y+y-z| I knew this was true because, but I'm looking for a generalization in a way that I could write in a proof. Can you say that when comparing two expressions of addition/subtraction that are...
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