Absolute Definition and 1000 Threads

Homework Statement If I have a expression like 5lx+2l, can I multiply the 5 with x+2? Homework Equations The Attempt at a Solution I'm guessing that I can only do this if the number in front of the absolute expression is a positive number. Because if -5lx+2l=-10 then multiplying...

Homework Statement I'm given this series and asked whether it converges, absolutely converges, or diverges. Ʃ(n=0 to infinity) [2(-1^n)(3^(n+1))]/5^n Homework Equations The Attempt at a Solution The answer states that it is absolutely convergent, and that it converges to 15/4. Everything...

so I understand the basic premise of differentiating a first ODE, or I thought I did. I have the equation y'-y=abs(x-1). I have no idea of how to go about this. Can someone walk me through how to do this? I'm attempting to study for a test and this is one of the practice questions he gave us so...

Homework Statement [abs(x)]/[abs(x+2)]<2 Homework Equations The Attempt at a Solution case 1: [abs(x)]/[abs(x+2)]<2 case 2: [abs(x)]<2[abs(x+2)] is this right so far? if so, why is there two cases and what do i do next?

Atoms at "Absolute 0" Hi everyone, I'm in high school right now so sorry if this question seems stupid or blatantly obvious to most of you, but at absolute zero, I understand atoms in a material cease to move and lose all kinetic energy between atoms, but what about the atom on a subatomic...

I was further looking into the Cauchy schwarz inequality and i got to a statement as follows: A·B ≤ |A·B| However, when I tried to prove this using numbers on paper, I wasn't sure if the absolute value bars distribute among each term, which would lead to |A|·|B|, or if the final product is...

Homework Statement Please show that the absolute derivative is a vector field along ##\gamma##, i.e., ##(\frac{d\lambda ^{a'}}{du}+\Gamma^{a'}_{b'c'}\lambda^{b'}\frac{dx^{c'}}{du})=X^{a'}_d(\frac{d\lambda ^{d}}{du}+\Gamma^{d}_{ef}\lambda^{e}\frac{dx^{f}}{du})## The Attempt at a Solution I...

The terms "absolute" and "relative" In discussions about relativity I use the term "absolute" as a synonym for "frame invariant" and "relative" as a synonym for "frame variant". I went to look for an authoritative definition and could not find one, so I am a little concerned. Is my usage...

Is this a correct a way of thinking for solving absolute value equations? Say I have |2x+6|-|x+3|=|x| and want to solve for x, then I have: For |2x+6| 2x + 6 if x ≥ -3 -2x - 6 if x < -3 For |x+3| x+3 if x ≥ -3 -x-3 if x<-3 For |x| x if x ≥ 0 -x if x < 0 Am I supposed to look at...

The equation |x-3|=-2 is given. Find the possible value(s) of X. I don't understand how it could equal a negative number but here is my weak attempt. |x-3|= -2 -|x-3|= 2 -x+3=2 -x=-1 x=1 I substituted x=1 into the equation and all I got was 2 as the answer. Any help would be...

I don't mind according to whose mechanics like einstein or Newton but what exactly is acceleration truely..If 2 bodies accelerating at same speed,then do the first body appear stationary for second and viceversa or is there any fictious force acting on them..?

Just a general question with absolute values: Is it possible to have an absolute value of this form: | f(x) - L | < -L (the minus sign is meant to be there) and if so how can I convert it into expanded form? i.e: -L < f(x) - L < -L or something of that form.

The variance equation basically sums up all the distances between each data value and the mean of the set. The interesting thing is that each distance and squared for a reason that I believe is to make the distance positive, but why don't the statisticians just take the absolute value of each...

Homework Statement ∫[|2x-1|] evaluated on the interval [1,-1] Homework Equations The Attempt at a Solution I know we must split it into two equations ∫ from [a,c] + ∫ from [c,b] and in absolute value one is negative and one is positive, so it will be 2x-1, and 1-2x my...

Hi everybody, I'd love to pick your brains about a problem in (seemingly?) linear algebra I've run into, trying to find the most efficient algorithm for solving a set of linear inequalities involving absolute magnitudes. During my research I've run into a problem that involves solving a...

Just a silly idea i have, please debunk it since i cannot figure it out: The Thought Experiment: Provided to us is a spacecraft equipped with a particle acceleration and detection systems. The craft is set on a course where it would not be interrupted by any interstellar objects and...

This could be very basic question, nevertheless its troubling me In Feynman's lectures, he says that though motion is relative, there is an absolute motion between 2 frames. A high velocity mu-meson when moved linearly or circularly would live just as longer than stationary one. Or a twin in a...

Homework Statement http://i.minus.com/i61zvy2BbtqkI.png Homework Equations One can factor the polynomial to (x-1)^2 The Attempt at a Solution After factoring the polynomial, I integrate (x-1) given the bounds of 0 and 1. I get -1/2. The solution manual says the answer is...

What is beyond Cantor absolute infinity? Then can you imagine what is neither beyond nor not beyond, which is we can't even say that 'the Being is beyond the universe or beyond infinity' to that particular Being? And what is neither singular/oneness nor multiplicity?

Like absolute zero, is there an absolute maximum temperature?

Homework Statement Given that \epsilon> 0, why is it, that \left | x_{n} -L\right |< \epsilon implicates that x_{n} > L-\epsilon ? Homework Equations The Attempt at a Solution

Homework Statement \sum from n=1 to n=\infty (1 + \frac{x}{n})n2 Determine the values of x for which the series converges absolutely, converges conditionally and diverges.The Attempt at a Solution So i tried using the root test for the absolute value of (1 + \frac{x}{n})n2, but it was...

Homework Statement Calculate Absolute Pressure? (1) A Lake has average temperature of 10°C and a maximum depth of 35m. The barometric pressure at the lake is 598mmHg. At the deepest part of the lake, determine the absolute pressure in Pascals. Specific weight of the water in the lake...

Homework Statement Minimize |2x1-3x2| subject to x1+x2≤5 -x1+x2≥-1 x1≥0, x2≥0 (a) Solve the problem graphically. (b) Formulate a linear program that could be used to solve the problem. Use software to solve your LP and show how to reconstruct a solution to the original problem...

Homework Statement Find the absolute maximum for f(t) = -t^3 + 3t^2 + 400t + 5000, t is between 6 and 20. Homework Equations f'(t) = -3t^2 + 6t + 400 The Attempt at a Solution I know how to find this - when the function can be perfectly factored. Yet some problems occur here...

I think the experiment of Newton's bucket is wrongly criticized.They deny the absolute velocity,it is right ,but they agnore the absolute nature of motion,which is not relative to other system,but is relative to the thing itself at the previous adjoining instant.Such as the expanding of universe...

Why does the half of the absolute value of a matrix formed with its coordinates give the area of a triangle? I don't see any similarity between that and the heron's formula.

Using the fact that the interval $\displaystyle\left[2k\pi+\frac{\pi}{4},\ 2k\pi+\frac{3\pi}{4}\right]$ contains an integer, prove that $\displaystyle\sum\frac{\sin n}{n}$ is not absolutely convergent.

Prove that if $\displaystyle \left|\frac{a_{n+1}}{a_n}\right|\le\left|\frac{b_{n+1}}{b_n}\right|$ for $\displaystyle n\gg 1$, and $\displaystyle\sum b_n$ is absolutely convergent, then $\displaystyle\sum a_n$ is absolutely convergent.

For absolute value of x, f(x) = lxl To prove continuous, I can express it as a piecewise function of x if x>0 and -x if x<0 and then I can take the limit of each as x approaches 0 from the negative and positive sides. Both limits give zero, and f(0) gives zero, so continuity is...

Let $\{a_n\}$ be a sequence, and $\{a_{n_i}\}$ be any subsequence. Prove that if $\sum_{n=0}^\infty a_n$ is absolutely convergent, then $\sum_{i=0}^\infty a_{n_i}$ is absolutely convergent. My attempt: $\sum |\ a_n|$ is convergent. $b_n=\left\{ \begin{array}{rcl}|a_{n_i}|\ &\text{for}& \...

I know that magnetic force due to a current carrying wire on a test charge moving w.r.t the wire(along the wire), can be interpreted as the electrostatic force if we use the first order relativistic corrections for Time Dilation or Length contraction of the charges of the wire, in the frame of...

Hello all, I am trying to figure out how to solve for the complex conjugate of the following: (-0.5)^abs(x) Thanks for your help. -Brian

Hello everyone, I'm posting here since I'm only having trouble with an intermediate step in proving that \sqrt{x} \text{ is uniformly continuous on } [0, \infty] . By definition, |x - x_0| < ε^2 \Longleftrightarrow -ε^2 < x - x_0 < ε^2 \Longleftrightarrow -ε^2 + x_0 < x < ε^2 + x_0 1...

Homework Statement Show that if bn→b, then the sequence of absolute values |bn| converges to |b|. Homework Equations The Attempt at a Solution I've been proving various properties of limits, including product of limits and sum of products, but have been having trouble making...

Homework Statement I am wondering if the general approach to these proofs involving absolute values and inequalities is to do them case-wise? Is that the typical approach (unless pf course you see some 'trick')? For example, I have: Prove that if |x-xo| < ε/2 and Prove that if |y-yo| <...

Write as one inequality with an absolute value x<-5 or 8<x not sure how you introduce the absolute value in this to solve it. thanks ahead

Homework Statement Evaluate ∫(1)to(-1) l sin(x) l dx Homework Equations The Attempt at a Solution If I just leave it like this, is it wrong? 1. ∫(1)to(-1) l sin(x) l dx = l -cos (x)l 2. l -cos (1) l — l -cos (-1)l = 0 - 0 = 0

Homework Statement Suppose f is the function defined by f(x) = l x-1 l Sketch the graph of y = f(f(x)) Homework Equations The Attempt at a Solution It's not so much sketching the graph that is the problem as much as it is figuring out how to set up the equations. How do I put an...

Hello everyone, Glad to be a new member of this superb forum :) In one of my physics classes, I have to construct an H-R Diagram. Now, this does not seems too challenging, and I'm sure it isn't. I was wondering if someone could kindly guide me in the right direction without giving me an...

I'm doing some practice problems, and with the help of my solutions manual and wolfram alpha I've worked out a solution to (x+1)\frac{dy}{dx} +xy = e^{-x} However, I don't understand why we can drop the absolute value bars when we calculate the integrating factor: e^{\int...

Homework Statement Lab 1: Question 6. (Note: each time you do this problem, the numbers will be different.) I want to measure accurately the time it takes for the drum of my clothes dryer to make one rotation. Since the door on the dryer is made of heat resistant glass, I can see the...

Suppose I want to compute tthe integral: \int_{-\infty}^{\infty}\frac{\textrm{sech}\hspace{0.1cm} x}{x^{2}-2|x|+1}dx Can I compute this integral via contour integration? The only way that I have thought of is to split up the domain: \int_{-\infty}^{\infty}\frac{\textrm{sech}\hspace{0.1cm}...

Let f(x) = |x|/x a. What is the limit of f, as x approaches 0 from the right? b. What is the limit of f, as x approaches 0 from the left? c. Hence, what is the limit of f, as x approaches 0? ------------------------------ The best way to evaluate limits involving absolute values is to use...

Dear Forum Users, I have got more math question rather then the physics question. Does someone know if: \mid d(x)\mid^2 equals just d(x), here d(x) is just the Dirac delta ? best regards, nykon

Homework Statement http://www4c.wolframalpha.com/Calculate/MSP/MSP621a026b7befdf1f1d00003b707661e1i20i4e?MSPStoreType=image/gif&s=55&w=126&h=38 Homework Equations limit x->3- (3x-9)/((abs(3x-9))The Attempt at a Solution I don't understand how to find the limit of absolute values..

Homework Statement Consider the manometer in the figure. If the specific weight of fluid A is 100kN/m3, what is the absolute pressure, in kPa, indicated by the manometer when the local atmospheric pressure is 90kPa? http://www.composmentisconsulting.com/2-61.jpg Homework Equations...

Homework Statement Problem is very simple but the textbook used for this class is complete garbage and has confused me to no end. a) Convert the following absolute power gains (dBm) to decibel power gains (dB). 10^-3 dBm, 2^n dBm b) Convert the following decibel power gains (dB) to...

As stated in SR, mass of the object increases with its velocity right? Lets assume that all the objects in the universe have consciousness and they all know what their rest mass is...(Leave photons out of the argument).. And also assume they all can measure their own mass at any instant...

Trig identity with natural logs and absolute value?? Homework Statement -ln|csc(x) + cot(x)|= ln|cscx(x)-cot(x)| Homework Equations The Attempt at a Solution I got that csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x), giving me a common denominator, added together I have...