Absolute Definition and 1000 Threads

Hello, I am having difficulty solving the following integral: \int^{\infty}_{-\infty}e{-(a|x|+ikx)}dx I have tried to use an explicit form of the absolute, eg. -(a|x|+ikx) = \left\{\stackrel{-(ik+a)x\ x>0} {-(ik-a)\ x<0} Does this allow me to separate the integral into a sum of two...

Homework Statement y= l sin x l < absolute value of sinx Homework Equations The Attempt at a Solution y= l sin x l= sinx, if x>0 -sinx, if x< 0 0, if x=0 I get that part, but when i draw the graph I don't get it

Homework Statement Solve (x+2)/(x+1) -2 < 0 Homework Equations LCD: x + 1 The Attempt at a Solution (x+2-2x-2)/(x+1) < 0 (-x )/(x+1) < 0 But somehow, I got the wrong answer. The answer is (4, 7]. But I don't know where I went wrong.

Homework Statement For the function y= |x2-4x+3| a. Sketch the function b. Is the function continuous? Explain. c. Is the function differentiable everywhere? explain d. find gradient of curve at the point where x = 3/2 Homework Equations chain rule, differentiating... The...

Homework Statement *Sorry I could not get the math symbols to work properly so I did it by hand. I hope this isn't too much trouble. Prove: | sqrt( x ) - sqrt( y ) | <= | sqrt ( x - y ) | for x, y >= 0 Hint: Treat the cases x >= y and x <= y separately. I am new to proofs and we can't use...

I know that in Newtonian mechanics an inertial frame of reference moves relative to absolute space. But why does Newtonian mechanics include the contention that two inertial reference frames move relative to each other? It seems that if you have an absolute reference frame then there is no...

Homework Statement [PLAIN]http://img704.imageshack.us/img704/453/50838240.jpg i have trouble with absolute function, can somebody help me how to start

Why does |e^i| = 1 ?

Excuse me for my english; Decide for all the x so this works out; ((2x-7)/(x3+3))<(9/x)<=x²-5x+9 where "<=" is the same as "and =". Having some troubles getting the right values between (9/x)<=x²-5x+9, but otherwise it's fine.. hope you can help me!

I solved this absolute value equation and I am confuse about the answer given in the book for this question, the answer in the book is x > = 0 or x = -2/3 please tell me how can I get this answer from the following solution. Please tell the method which should be true for all such type of...

Suppose we have this absolute value question | x-3 | = 3 – x If we solve this question we break it as X - 3 = 3 – x or -(x - 3) = 3 - x Now if we solve it we come to know that the part on right is true for all real numbers And the part on the left is true for only 3 I also have read that...

Homework Statement Let X be a continuous random variable with median m. Minimize E[|X - b|] as a function of b. Hint: Show that E[|X - b|] = E[|X - m|] + 2 \int (x - b) f(x) dx , where the integral is from b to m. Homework Equations The Attempt at a Solution I wanted to try a...

I started posting to what seemed to be a related thread here: https://www.physicsforums.com/showthread.php?p=2825641&posted=1#post2825641 After concluding I was hijacking another thread, I am posting here. The concept is I think that, in theory, one can determine absolute speed. Am I the one...

Homework Statement Solve the inequality and sketch the graph of the solution on the real number line. Homework Equations |x - a|< or equal to b, b > 0 Let us imagine that the ">" and "<" signs also include "equal to" except for the condition, b > 0, in order to solve this...

Homework Statement I do not have a specific homework problem, but could someone please clarify this for me? QUESTION: When you have an absolute maxima (or minima), how can you tell if it is ALSO a relative maxima (or minima)? I understand how to find absolute extrema on a closed...

regarding the problem of time in QG, Is time absolute or dynamical in LQG? string theory? How does LQG and string theory deal with time in singularities in the center of black holes?

Relativity says that there is no absolute simultaneity. Quantum mechanics with its entanglement seems to imply absolute simultaneity. And in between these two I am the one who gets confused. :smile: :confused: Please Help.

Homework Statement I have E(a) = 0, E(b) = x but E(|a+b|)=?? where E is the expectations operator and x is a known constant which is greater than zero. Homework Equations Any one know how I would go about determining E(|a+b|)?

Hi, I'd like to know how does electromagnetic radiation behave at absolute zero temparature ? pls let me know. Thanks in advance !

Hi, With a meridian circle, you can determine the latitude of your location (Horrebow-Talcott method) but also deriving time if you know the right ascension of a star. However, I'd like to know how to determine right ascension of a star with a meridian circle. If you know the right...

Is there an equation for calculating the distance of a star if you have the values for apparent visual magnitude and absolute visual magnitude?

Greetings, I have heard that one can not know one's absolute velocity, only one's velocity relative to other objects. But wouldn't the cosmic background radiation be blueshifted in the direction of motion and redshifted in the oposite direction? Thanks

I've been thinking about getting a tattoo. I was considering getting the infinity symbol inside of an absolute value. Or the absolute value of infinity. Whichever you prefer. How mathematically correct is that? The absolute value of infinity simplified is infinity is it not? Will I completely...

http://www.sciencedaily.com/releases/2010/06/100627072458.htm According to the above article, light was brought to a complete stop during an experiment. What confuses me is that, if light has no mass, and is then manipulated to have no velocity either (which means there is no frequency and...

Homework Statement I saw this in my real analysis textbook and I have been trying to understand how this equation \left | x-c \right |< 1 you can get this: \left | x \right |\leq \left | c \right | + 1 Homework Equations I wanted to know what steps made this possible ...

I'm having trouble understanding angular momentum and how it relates to SR/GR. To keep it simple, if I'm in space and all matter and energy is removed (ie. reference frames) and I start rotating at a specific velocity will I feel my arms and legs being pulled out? If the only possible frame of...

Sorry if this question seems more philosophical than scientific. It's my first post in this forum. I love learning about the way the universe works and I always have lots of questions :-) Alright, so to my point. It seems like the theory of relativity says that the faster you move (plus how...

Homework Statement By comparing with the luminosity of the Sun, calculate the absolute magnitude of a 60W lightbulb. [THe absolute magnitude of the Sun is +4.75; you may ignore colour differences] Homework Equations m-M=5log(d/10pc) f = \frac{L}{4\pi d^{2}} m1 - m2 = -2.5long(f1 / f2) The...

Homework Statement If a,b are real numbers and b does not equal zero show that |a|=sqrt(a^2) and |a/b|=|a|/|b|. Homework Equations I know that |ab|=|a||b| and a^2 = |a|^2 The Attempt at a Solution Attempt at showing that |a|=sqrt(a^2): |a|=sqrt(a^2) |a|^2=(sqrt(a^2))^2...

Hi, I came across a book which looks at a problem like \lim_{x \to 0}\frac{1}{x} So you approach from 0-, and get -∞, approach from 0+, get ∞ Then it would write the answer as \lim_{x \to 0}\frac{1}{x} = \left| \infty \right| It looks bizarre to me. How do you parse this? Is...

How to compute \beta = arg min_\beta \sum_{i=1}^N {|y_i - x_i^T \beta|

Consider this thought experiment. Second postulate of SR (invariance of c) says that the speed of light is measured the same for all inertial observers regardless of their relative KE. To better understand what that means I try to imagine how would that look from a perspective of the moving...

Homework Statement how do I solve this? I am confused... |2x - 1| = x^2 Homework Equations The Attempt at a Solution when i tried it I ended up with a solution set of (1,-1). But the official answer is quite different so I am confused!

"Absolute" light speed or velocity or both? Consider an inverse of Einstein's light clock. On a cartesian plane in a vacuum, a beam of light emanates from the origin at 45 degrees with velocity c. Is it OK that the x and y component velocities are each less than c (i.e. c divided by sqrt 2)...

Homework Statement If f(x) is equal to... x+9 if x<-3 -2x if |x|\leq 3 -6 if x > 32. The attempt at a solution The first and third "segments" of when the function is defined as being x+9 and -6 are pretty straightforward to me, however I am unaware of the significance of the placement of the...

Homework Statement Find the CDF of |X|, given that X is a random variable, uniformly distributed over (-1,3). Is |X| uniformly distributed? If yes, over what interval?Homework Equations The Attempt at a Solution I found so far that: Setting Y=|X| Then: Y \in (1,3) F_{Y}(y)=P\left\{Y\leq...

Homework Statement 1 ⌠ | 10^(1/2)*(x^5)+(5*x^(1/5)) | dx ⌡ −1 Homework Equations once the absolute value is gone you can just integrate the function The Attempt at a Solution how do you get rid of the absolute, and how do you then integrate it, do you use the product rule...

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...

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...

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''?

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...

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...

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...

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...

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...

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...

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...

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...

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

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...