Absolute Definition and 1000 Threads

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...

How we can integrate this (without integration limits) sqrt (|x|)

ie: in the figure theta 3 i got i want theta 2 what formula would i use

STUPID QUESTION ALERT! Is spacetime an absolute reference frame?

Homework Statement Let f(x, y) = |xy|. I want to prove that f is not continuous at (0,0). The Attempt at a Solution To prove that f is not continuous at (0,0) I think I need to show that \lim_{(x, y) \to (0, 0)}|xy| \neq 0 I'm a little confused about the |absolute value|...

This is a physics problem, but I only need help with the calculus portion of it. I was having trouble figuring out how to split the integral to properly integrate. Homework Statement Homework Equations \int\stackrel{\infty}{-\infty}(x/x_0)e-2|x|/x_0dx where x_o is a constant...

Hi everyone; I've got this question concerning absolute value, although I understand the concept of absolute value, I can't quite understand why option B is bigger than option A. I would really appreciate some explanation on the following question: I am trying to post it in Latex, but in case...

sin|x + y| = ? cos|x + y| = ? Is there any formula for these?

Homework Statement y = 2 − x^2, y = |x| sketch and find the area of the region determined by the intersections of the curves Homework Equations regular f - g of integral The Attempt at a Solution The absolute value puzzles me. How would it work then? I mean we know how each...

Hello all, I am finding a distance to a cluster via Main Sequence fitting, and I don't know where to find an absolute color - magnitude diagram ( B-V, and V ). I can be from any star cluster, or sky region, as long as the magnitudes are absolute. I need the data tables, not just a pretty...

Homework Statement Determine whether the series converges absolutely, conditionally, or not at all. a) \Sigma (-1)nn4/(x3 + 1) b) \Sigma sin(x)/x2 Homework Equations The Attempt at a Solution a) positive series is n4/n3+1 .. do i do comparison test ?? b) |sin(x)|/x2...

Can anyone tell me the general procedure in doing the following procedure? f(x,y)=xy^2 with domain x^2+y^2\leq4 Find it's absolute max & absolute min. Okay, here is my thought procedure, tell me what I can fix. So I would basically say, find the partial derivatives with respect to x and y...

Find the absolute min & absolute max of f(x,y)=xy^2 with domain x^2+y^2\leq4 Please help

Homework Statement Calculate your experimental value of absolute zero , how does your experimental value compare to the theoretical value -273C? Homework Equations T_abs=(S1*T2-S2*T1)/(S1-S2) The Attempt at a Solution This is all part of a lab. I'm not asking people to do any...

In a lot of compilations of standard integrals (my Calculus book does this, Wikipedia does this), a lot of the integrals of trigonometric functions have an absolute value in their solution which seems out of place to me. For example, take the integral \int dx \cot{x}. My Calculus book says...

What does QM have to say on the ontology of time? Is time absolute or relative? What does quantum entanglement have to say on the subject?

Homework Statement I need to find where these intersect: y = |x| 3y - x = 8 Homework Equations The Attempt at a Solution I equate them: |x| = (1/3)x + (8/3) |x| - (1/3)x - (8/3) = 0 |3x| - x - 8 = 0 |2x| - 8 = 0 |x| = 4 Is that right? How do I get the other solution?

Hey, here's the question: "If a gauge reads -295mmHg where athmospheric pressure is 101.7 kn/m^2 and the vapor pressure is 2.8 kN/m^2, what is the absolute pressure?" I converted the gauge pressure to 39.36 kN/m^2 but where do i go from here? I know the equation is p_gauge= p_absolute -...

Hey, here's the question: "If a gauge reads -295mmHg where athmospheric pressure is 101.7 kn/m^2 and the vapor pressure is 2.8 kN/m^2, what is the absolute pressure?" I converted the gauge pressure to 39.36 kN/m^2 but where do i go from here? I know the equation is p_gauge= p_absolute -...

Hello... If time stops at the event horizon of a black hole..which means there is no motion happening or can be observed..does that not mean that the centre of a black hole is a place of absolute rest? Could such a place of ab/rest 'move' thru the cosmos (basically a black hole which is a...

Find the relative extrema of f(x)=|3x-x^2|. Normally you solve f'(x)=0 to find the critical points, in that case we have 3-2x=0 => x=3/2. However there are two other relative extrema that I cannot find by calculus as the absolute nature of f(x) has confused me. Indeed doing a sign analysis on...

I was looking at a derivation of entropy expressed as an absolute probability: S = -k. SUM P.lnP (What is the name of this by the way?) In the derivation, it makes the following statements which I really just don't get! U = SUM E.P so therefore dU = SUM E.dP - SUM P.dE Where does...

I'm trying to wrap my head around how rotational frame dragging affects the centrifugal force of a massive, rotating body and was hoping someone could explain this concept to me better. If I am confused on any of the points below please let me know. It is my understanding that there is no...

Homework Statement Hi all I have f(x)=|x|. This I write as f(x) = -x for x<0 f(x) = x for x>0 f(x) = 0 for x=0 If I want to show that f(x) is not differentiable at x=0, then is it enough to show that f'(x) = -1 for x<0 f'(x) = 1 for x>0 and from this conclude that it is...

What is meant when the potential difference of a point in space is quoted? (my book calls it absolute potential). What "difference" is being referred to (only one point is being referenced)?

Hi everyone, I am new to this forum - happy to meet you! :-) Background to my questions: According to quantum physics, there is no "absolute stillness" (but always some "quantum noise"). This seems to be one of the implications of Heisenberg's uncertainty principle (because if there was...

I was thinking, if time passage varies with speed would the speed of atoms random movement (temperature) affect time? For example, if the universe is expanding, as some predict, it will eventually reach a state where everything will reach very near to absolute zero, or maybe absolute zero. If it...

Isn't the distance between two atoms where nothing exists, no atoms or subatomic particles, absolute vacuum? a place where nothing exists?? I am not too educated in such physics, so please do explain what you say

For example, what happens if you put an apple in space? Or what happens when animals (or people) are frozen to very low temperatures?

Homework Statement Doing some problems from textbook, I need to determine whether the series is absolutely convergent, conditionally convergent, or divergent. n!/n^n I plugged it into WA, and it says the series doesn't converge, but I'm not sure how to figure it out. Homework...

Let's say we have two perfectly rigid spheres. One is at rest and the other is moving toward it with some differentiable velocity. When they collide, the first sphere will start moving with infinitesimal velocity and the second will reduce its speed by an infinitesimal amount. But since the...

Homework Statement Given: |A|+A+B=15 and A+|B|-B=13. What is A+B equal to? Give all possibilities. Homework Equations The Attempt at a Solution I solve for both absolute variables. So, A=15-A-B or A=A+B-15 and B=13-A+B or B=A-B-13 Firstly, I solve for A. A+A=15-B...

Homework Statement In Spivak's Calculus 4e, he defines absolute value as: |a|= a,\qquad a\ge 0 \qquad \text{ and } \qquad -a,\qquad a \le 0 Did he really mean to include the '\le ' and not just '<' ? I know it does not affect the answer, but I didn't think that you could...

\int^{\pi/2}_{0}|sinx-cos2x| dx Hi guys i can't seem to get the correct answer for this. What i did was draw the graph of sinx and cos2x and for 0 to \pi/6 i use cos2x-sinx since cos2x is higher. From \pi/6 to \pi/2 i use sinx-cos2x. However i am not able to get the same answer as my book can...

Homework Statement Find the abs min/max values of the function f(x,y) = e1-2x2-y2 on the closed and bounded region x2 + y2 <= 1 The Attempt at a Solution First I have to find the critical points Dfx = (-4x)e1-2x2-y2 Dfy = (-2y)e1-2x2-y2 Clearly e1-2x2-y2 cannot equal 0...