Absolute Definition and 1000 Threads

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 am reading through my introductory course notes, and am given a question I don't understand how to answer. A rectangular tank contains fresh water inside it to a depth of 0.5m. The tank is 1m long and .7m wide. a) calculate gauge pressure at the bottom of tank b)...

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...

Homework Statement Part of a problems asks us to show that for a general function f(|r1-r2|)=f(R) that Div[f] only with respect to r1 is the same as Div[f] only with respect to R Homework Equations f(|r1-r2|)=f(R) The Attempt at a Solution I'm really unsure where to start, but I...

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(uncertainty1 + uncertainty2)...

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...

Absolute Zero, about -273.15ºC, is the coldest known temperature possible, where matter it's self, stops moving, and energy can't build up. But, could there be...say, an absolute ∞? Or like...and Absolute energy? Could these be physically possible, and where would these things be found. What...

Homework Statement Prove that, if f is continuous on [a,b] and ∫ab= l f(x) l dx = zero then f(x) = 0 for all x in [a ,b]. Homework Equations Hint- from book- Section 2.4 Exercise 50 Let f and g be continuous at c. Prove that if: (a) f(c) > o, then there exists delta > o such...

Homework Statement Let p>0. What is the derivative of |x|^{p}? Homework Equations The Attempt at a SolutionI know that if p is even, then the derivative is just px^{p-1} . But what if x is odd? Would it turn out to be some piecewise function, such as px^{p-1},\: if x \geq 0 and -px^{p-1}...

Determine the absolute uncertainty of the prism's volume. The uncertainty of each measurement is +/- 0.5mm. The length of the prism is 142mm, width is 86mm and the height is 151mm. Thank you!

Homework Statement We are given that the reaction time for pressing the stopwatch is 0.2 s (we are measuring 15 swings, t15 = 30.45 s) and we need to determine the absolute error in one swing. The Attempt at a Solution My question here is whether the absolute error for those swings is then 2 x...

According to theory of relativity there is no absolute standard of rest. Now, if Alice and Bob are two observers floating in space, so that Alice thinks that she is at rest and Bob is moving away from her at a speed comparable to that of light and Bob thinks that he is at rest and Alice is...

Homework Statement If \suman2 and \sumbn2 converge show that \sumanbn is absolutely convergent Homework Equations The Attempt at a Solution I think I should do something with the statement 2ab\leq a^2 + b^2

Homework Statement I'm trying to prove that Sp|f| - sp|f| \leq Spf - spf Where P is a partition of [a,b] and f is function that is riemann integrable. Homework Equations The Attempt at a Solution So I get to a point where M = supf(x) and m = inff(x) then |M|(b-a) - |m|(b-a)...

I understand MAD, but I cannot figure out this question. Here's the information. Daily high temperatures in St. Louis for the last week were as follows: 92, 91, 94, 95, 96, 88,90. The mean absolute deviation based on a 2-day moving average = 3.20 How in the world is it 3.20? I've tried...

Hi everybody, I would like to begin with apologizing for anything stupid I might say or ask because I am not a qualified physicist. I'd like some minutes of your time because i have a question that's been on my mind far too long and i would really like some help with this. Am I correct when I...

When it is said that the universe is, for example, 9 billion years old, is it the same everywhere else in the universe? Do the distant quasars that we see know that they are the same age as we figure they are? And what defines the “edge” of our universe. The most distance object that we can...

Alright, I'm completely confused. I was given a study guide for my Algebra 2 exam(this isn't homework...) and one of the questions was 2|3x+5| < 16 I've seen the absolute value, but never seen a number in front of it...How do I solve this ?

i am in the 9nth grade and i am intrigued by the idea of Absolute zero and the phenomenas, my question is what will happen if we reach absolute zero? i know that molecules slow down until they stop, but i don't understand one thing, what is keeping the atoms together, isn't it energy. is there...

Homework Statement Let there be m independent samples, each of size n, and are drawn from a population of size N using a design D(S,P). Based on the ith sample i = 1, 2, ..., m, let \hat{\theta_{i}}(s) denote an unbiased estimator of \theta. Let \hat{\theta} =...

Here is my question, starting from a suggested experiment that reminds a known example that Einstein gave about special relativity including a moving train, two mirrors inside the train and a light beam reflected between the mirrors (this suggested thought experiment described here only reminds...

i am not exactly sure what happens when the temperature almost reaches absolute zero how things react to this drop and what are boson ( sorry for spelling errors)

Homework Statement show that if f is increasing on [a, b], then f is absolutely continuous if and only if for each \epsilon > 0 there is a \delta > 0 such that for each measurable subset E of [a, b], m*(f(E)) < \epsilon if m(E) < \delta. Homework Equations The Attempt at a Solution

I never really understood why using the Root Mean Square of negative data is the preferred method of finding the average of the data as opposed to taking the absolute value of the data and taking the average (arithmetic mean) of that. The example that recently made me wonder about this is...

Hi all. For a project I am doing, I need to find a motor with an encoder that we can use to detect the exact angular position of the shaft at any given point in time. I'd like to see if there is any motor out there with absolute feedback from the encoder - i.e., that I would be able to read...

Homework Statement A constant-volume gas thermometer is cal- ibrated in dry ice (which is carbon dioxide in the solid state and has a temperature of −80◦C) and in boiling ethyl alcohol (78◦C). The two pressures are 1 atm and 1.542 atm. What value of absolute zero does the cali- bration...

Homework Statement find all values of p in R for which the given series converges absolutely. \displaystyle\sum\limits_{k=2}^{\infty} \frac{1}{klog^pk} Homework Equations Ratio Test Or Root TestThe Attempt at a Solution So I tried using the ratio test and get: \mathop {\lim }\limits_{k \to...

Homework Statement Find the absolute maximum and the absolute minimum of the function, f(x,y) = x^2 + 2xy - y^2 on the region bounded by, x = \sqrt{1-y^2},y=x \text{ and } y=0 Homework Equations The Attempt at a Solution See figure attached for my attempt. Everything...

The below text is not a result of coherent thought. It consists of random pieces. I'm sure you would be able to connect them. If there is absolute religious system, then it's won't too much exaggeration to say that I live in a far too religious atmosphere where almost every individual takes...

Homework Statement Find the maximum value of the function f(x, y) = x^{2} - y^{2} + x considering only points inside and on the boundary of the region bounded by the curve, x = \sqrt{1-y^{2}}, x=0 Homework Equations The Attempt at a Solution See figure attached for my attempt...

Homework Statement Find the maximum value of the function f(x, y) = xy(3 − x − 2y) on the triangle R bounded by the positive x- and y-axes and the line x+y = 1. Assume that f(x, y) has no critical points in the interior of R. Homework Equations The Attempt at a Solution See...

Is the uncertainty principle enough to prove that absolute zero is unachievable? i.e. a particle can't be said to have exactly zero energy, because it can't be said to have exactly any amount of energy.

Two rays of light of wavelength 650 nm and 420 nm are normally incident on a different grating. If the grating has 5000 slits/cm, what is the angular separation of of the two light rays' second order maximum. -Need to find the absolute value of theta 650-theta 420 I know I need to use...

Alright, Could you use magnets to slow matter down enough to reach "near" absolute zero? Heres how it would work. You would have a range of magnets in a chamber, and you would inject the chamber with protons. The magnets are comeing from all directions forcing the proton to stay still. Then...

Homework Statement My brain hasn't been working lately so if you see something weird in my proof pardon me and advice me against it. So the problem states: Show that an even degree polynomial has either an absolute max or min.Homework Equations The Attempt at a Solution Let f(x) be an even...

Show that the kinectic energy of a three-dimensional fermi gas of N free electrons at absolute zero is (Mathematica code used) u = 3/5 N Subscript[\[Epsilon], F] Now I know total energy of N particles is this integral u = \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\)...

Hey. I have | tn - t | < M How can i show that t - M < tn thanks

I hear how people create superconductors by taking a metal and freezing it to Absolute Zero(0 Kelvin). What are some methods to get this sort of tempuature? Can anyone help?

If so, how did they become absolute to all mankind across cultures and terriotories?

I am having some issues with going about finding the max and min of trig functions over a set interval. Normally with finding the max and min of a function over an interval the first thing that I do is find the derivative of that function, Then i set the derivative to 0 and solve to find the...

Homework Statement i did it on paint and print screened to make it more clear what i did :) I am getting, as shown above, 0 for abs max and -15 for absolute min. But it wants -48 for abs min and i have no idea how to get that >:(

I have a problem in understanding the procedures of a solved example. It goes like this. \left ( \frac{z+i}{z-i} \right )^4 = -1 Therefor we can write: \left | \frac{z+i}{z-i} \right | = 1 From that we can see that z is a real number because: \left | z+i \right | = \left | z-i...