Absolute Definition and 1000 Threads

Homework Statement ∫ |x^2 -9| [0-4] Homework Equations The book answer states the same EXCEPT splits into [0-3] and [3-4]. Other problems split the integral perfectly in half for absolute values...why would it differ and are there rules to figure this out? Larson's Calculus has no...

Homework Statement Find the absolute maximum and absolute minimum values of the function (x^3)+(12x^2)-27x+9 on each of the following interval [-10,0] The Attempt at a Solution I got this and its saying its wrong. y'= (3x^2)+(24x)-27 factor: 3(x^2+8x-9) so x=-9 and x=-1 y''=6x+24...

Homework Statement given an = ( -1 )(n+1) / \sqrt{n} determine if the infinite series is Absolutely Convergent, Conditionally Convergent, or Divergent. Homework Equations I hope I have these theorems down correctly, please correct me if I'm wrong. If \Sigma|an| is Convergent then...

can a particle hold it's information at absolute zero?

Homework Statement Find all x in |5x-2| = 6x-12 The Attempt at a Solution http://www.wolframalpha.com/input/?i=Plot[|5x-2|+%3D+6x-12%2C{x%2C-1.5%2C1.5}] Notice how only x = 10 is a solution? So my question is, why isn't x = -14/11 a solution? I mean sure they don't...

[b]1. | (2-i)(3+2i)(-5-6i)(-7+3i) / (-4+i) | Homework Equations [b]3. I am pretty sure I am not computing it right but this is what i come up with. square root of 5* square root of 13* square root of 61* square root of 58 / square root of 17.

Special relativity upended our normal conceptions of space and time by postulating that the speed of light was absolute for all observers. So rather than the absolute space and time of Newton, Einstein postulated an absolute speed of light, which by necessity leads to a malleable space and time...

Homework Statement Let z,p,q \in \mathbb{C} be complex parameters. Determine that the Gamma and Beta integrals: \displaystyle \Gamma (z) = \int_0^{\infty} t^{z-1} e^{-t}\;dt \displaystyle B(p,q) = \int^1_0 t^{p-1} (1-t)^{q-1}\;dt converge absolutely for \text{Re}(z)>0 and p,q>0...

Homework Statement DIRECTIONS: Express the intercal in terms of an inequality involving absolute value. PROBLEM: (-4, 4) MY STEPS: 1: (-4, 4) 2: -4<x<4 3: |x|< 4 MY ANSWER Is that correct? Is step 3 correct? The only reason that I included that part is becuase it says...

Homework Statement Very embarrassing that I had problems with this. I managed to solved it at the end, but I am posting this for two reasons 1) I like someone else to work it out in a different method, I wnt to see what other approaches there are 2) Whether mine is taking too long or not. I...

So, a professor in class a about a year ago mentioned that opening a switch in a circuit that an inductor is providing power to would cause a breakdown in the air and a spark would jump across it because the current can't change instantaneously to zero in an inductor. Something just made me...

Hi, I have a general question regarding the integrating factor of first-oder linear DEs. All textbooks that I've seen (which aren't too many) simply drop the absolute symbol when the factor has the form exp(ln(abs(x))). This would evaluate to abs(x), yet the books use simply x. Why is that...

Homework Statement If the absolute value of a sequence, an converges to absolute value of A, does sequence, an necessarily converge to A? Homework Equations convergence: a sequence { an}n=1-->infinity, converges to A є R (A is called the limit of the sequence) iff for all є > 0, there...

Hi to all ! I have been doing some research in Godel's universe (I have just finished my first General Relativity course so I'm not an expert yet) and there is something which is still not clear to me. Can someone explain me why the fact of having a non vanishing angular velocity implies that...

So I'm going into a physics major next year, but lately I've been interested in electronics. Not enough to switch majors, but I'd like to take it up as a hobby at least. Unfortunately, I have absolutely no experience. I have the Circuit Analysis book that EE majors at my school use for the very...

I'm not a scientist, but I really enjoy reading the perspectives on these boards. I have some questions I hoping to hear a lot of perspectives on. I know absolute zero has never been reached, but in what ways are we attempting to find absolute zero currently? If, hypothetically, we were...

There are two space stations A and B which are at rest wrt to each other and separated by some distance x. Each space station has a light that randomly flashes. I am in a third space station, somewhere in the middle of A and B and at rest wrt to the other two stations. I see Station A’s...

Homework Statement Solve the IVP (x^2)y'' + 4xy' - 40y = x^6 for y(1) = 10, y'(1) = 1Homework Equations not so much "equations" but here I try to use variation of parameters to get the particular solution.The Attempt at a Solution FOR THE HOMOGENEOUS SOLUTION: using the substitution y = x^r...

I am reading Hayashi's paper titled "http://prd.aps.org/abstract/PRD/v19/i12/p3524_1" " (Phys. Rev. D 19, 3524, 1979). In Riemann-Cartan geometry, one can choose the Weitzenbock connection rather than the well-known Levi-Civita connection, so that Riemann curvature tensor vanishes while the...

Homework Statement Let R be a set of real numbers derived from rational numbers. And, let R* be a set consisting of all ordered pairs of the form (x,0) where x is an element of R. For a complex number z = (a,b) = a+ib, I've learned that the absolute value of z is the number...

Hi, Today in school I performed an experiment that went like this: We had a capillary tube with trapped air on the bottom, the top part was open to the atmosphere and, in between, there was some sulphuric acid. We heated the capillary tube and recorded the increase in volume of the trapped...

Let's say I have two (-) charged beams. According to observer 1: Beam 1 is shot at 0.998 c. Beam 2 is shot at 0.999 c. >> Therefore, the beams are moving in the same direction. Observer 2 is moving at 0.9985 c. Observer 3 is moving at 0.9995 c. According to observer 2: Beam 1 is shot at -0.143...

Homework Statement |2(2)^0.5 -3|+|3+(5)^0.5|=x Homework Equations why is the answer 6-2(2)^0.5 +(5)^0.5 and not 2(2)^0.5 + (5)^0.5 The Attempt at a Solution the answer multiplied - into the first absolute. why arent the other combos the answer?

Homework Statement [PLAIN]http://img845.imageshack.us/img845/1706/delta.png The Attempt at a Solution This question has come after a chapter on Dirac's delta-function although the question doesn't say use it. Could I use it? If not how do I do it directly?

Homework Statement solve for x: 5|7-3x|+2=4|7-3x|-1 Homework Equations The Attempt at a Solution 7-3x>0 -3x>-7 x<3/7 {x|x<3/7} quantity is positive {x|x>3/7} quantity is negative I have never solved an equation with more than one absolute value quantity in it and am not sure how to start...

I have heard it said that an object not feeling acceleration cannot determine if he is in motion unless he sees another object to compare himself too. But what if you had an apparatus that was made of two spheres. One inside the other. Perfectly centered on each other. The inner sphere emits...

Homework Statement I was trying to show that 1) |a+b|≤|a|+|b| 2) |a+b|≥|a|-|b| and find out how they were true when a,b>0, a,b<0, and a>0,b<0 Homework Equations 1) |a+b|≤|a|+|b| 2) |a+b|≥|a|-|b| The Attempt at a Solution For |a+b|≤|a|+|b| a,b>0 I got that |a+b|=a+b...

Absolute Convergence, Conditional Convergence or divergence... Homework Statement \sum_{n=1}^{\infty} \frac {(-2)^{n}}{n^{n}} Homework Equations \lim_{n \rightarrow \infty} | \frac {a_{n+1}}{a_n}| < 1 \;\; absolute\; convergence \lim_{n \rightarrow \infty} | \frac...

Homework Statement If the series \sum_{n=1}^{\infty}x_n converges absolutely, and the sequence (y_n)_n is bounded, then the series \sum_{n=1}^{\infty}x_ny_n converges.Homework Equations Definitions and theorems relating to series and convergence.The Attempt at a Solution If the sequence y_n is...

Homework Statement just a simple problem as an example dy/dx = y/x dy/y = dx/x Homework Equations The Attempt at a Solution dy/y = dx/x ln|y| = ln|x| + c then when I take exponents do I still have to include the absolute value bar |y| = |x|c

This is highly theoertical and I came up with it taking a standerized test. So without further adoo, What would happen if you to a cyrogenic chamber froze something to ablsolute zero and put it on a spacecraft moving at exactly the same velocity as the universe is. Thus canceling out...

When something is frozen fully, and the temperature is absolute zero -there is no entropy - but does that mean the "quantum jitters" are not occurring?

Hello friends, I am quite confused how an absolute function is called a continuous one. f(x) = |x| has no limit at x=0 , that is when x > 0 it has a limit +1 {+.1, +.01, +.001} and -1 when x <0 {-.1, -.01, -.001} that is the reason it's not differentiable (left and right side limits are not the...

I was just wondering. With the Twin Theory, with the person traveling at the speed of light causes them to age slower. So I wondered, does that mean that something would age faster if at absolute zero? Because I've heard that motion is relative to temperature, and time is relative to velocity...

According to Charles' law, volume decreases with temperature. Extrapolating down towards absolute zero, and the volume of the gas will be zero. How can this be possible? Surely any amount of gas will still have to take up some volume in space. Can multiple gas molecules really occupy zero volume?

Hi, as part of a project I needed a slim (<10mm) small diameter (<30mm) through hole absolute encoder that works at 100 degC. I wanted this to be able to determine a motorized valve position, so it needed to slip onto the gearbox output shaft between the motor and the valve. Anyway, I...

EDIT: On pg. 390 of Kreyszig's Functional Analysis text, we have: "If T is a bounded linear operator on a nonempty Banach space, then the series \sum_{k=0}^\infty \left( \frac{T}{\lambda} \right)^k converges absolutely for |\lambda| > 2\| T \|." The argument presented in Kreyszig...

Total "absolute" curvature of a compact surface Hi! Someone could help me resolving the following problem? Let \Sigma \subset \mathbb{R}^3 be a compact surface: show that \int_{\Sigma}{|K|\mathrm{d}\nu} \ge 4\pi where K is the gaussian curvature of \Sigma. The real point is that I want...

Homework Statement Im getting very confused with working out how to integrate the following double integral with an absolute value: \int^{2}_{-2}\int^{2}_{-2}\left|x^{2}+y^{2}-1\right|dxdy Homework Equations The Attempt at a Solution I know you have to split it down into where it...

Quick question (hopefully): I'm helping my girlfriend with some calculus homework over the phone and it looks like the book has a different answer for the derivative of an absolute value than I'm seeing in other places. I'm seeing it as (and I derived it myself to be) x/abs(x) whereas the book...

I explain my question through an example. If we brought down a GPS clock, would it show the normal time, because it was accelerated before launch, but it has been slowed down by time dilation? Or we have to accelerate those clocks in order to compensate for the time loss, till the signal from...

Homework Statement \Sigma from n=0 to infinity (-10)n/n! Determine the absolute convergence, convergence, or divergence of the series. Homework Equations In this section, it's suggested that we use the following to determine a solution: A series is called absolutely convergent if the series...

Homework Statement A cylinder in a car engine takes Vi = 4.50 x 10^-2 m^3 of air into the chamber at 30°C and at atmospheric pressure. The piston then compresses the air to one-ninth of the original volume (0.111Vi) and to 20.0 times the original pressure (20.0 Pi). What is the new...

Homework Statement I have this equation |2x+7| - |6-3x| = 8. The step I did is to replace the || with () and then solve the equation 2x+7-6+3x = 8 X = 7/5 But how do a go about solving for the second solution? With one absolute value I would |2x + 7| = 8 2x + 7 = +-8 2x = -7...

Hey Guys! I've frequently come by this forum and have finally joined it in hopes that I could get some more conceptual insight in understanding math. One thing that I have trouble with is absolute values. I understand that: |x|= \sqrt{x^2} .. and how it can be defined given restrictions on...

Hi guys, I have a little problem with this question: Determine the limit (x approaching infinity) \frac{|9-3x^{2}|}{x-2x^{2}} (Sorry, I'm not sure on how to use the Latex feature) Anyways, I've combed the forum and found a couple of threads that are somewhat related to my problem...

Homework Statement [PLAIN]http://img225.imageshack.us/img225/7501/complexh.jpg Homework Equations The Attempt at a Solution How do I show this absolutely converges?

Homework Statement Perform the calculation and report answer in proper scientific notation with absolute uncertainty 73.936(+ 0.19%) / [(0.00455+ 0.00096) + (0.011889(+0.73%))] Homework Equations Addition/Subtraction: Absolute uncertainty = square root(uncertainty[SIZE="1"]1 +...

Hello all, I am trying to solve a problem based on some computer programming task I am trying to solve, and I have encountered a situation I am having trouble continuing.. Given a function f(x)=|1-x| + |0.5-2x| ... How can I find it's minimum efficiently? This sum may extend to 4 or 5...

Homework Statement In manipulating transmission spectrum data from GaAs and InP I'm told to "Look up the refractive indices of GaAs and InP in the region of  = 1.0 micron, and use these to correct your experimental data for reflective losses and plot the corrected transmission T’ in...