Absolute Definition and 1000 Threads

when i am exploring a function eg. f(x)=|2x-6| can i treat it as two separate function all the way through, one to the left of x=3 and one to the right, and only at the very end, when i draw the graph connect them, ie draw a graph according to all the values i found from each side? will this...

Homework Statement I do not see how the two equations in each example are related, what should I do with them? (the l's are absolute value brackets): a) Let g(x) = 3x - 3 + l x+5 l. Find all values of a which satisfy the equation: g(a) = 2a +8 b) Let h(x) = l x l - 3x...

Let z be the complex number: x+iy. Then |z|^2=x^2+y^2 according to my book. But according to the general definition of absolute value, |a|=(a^2)^.5. So letting z=a=x+iy. |z|^2=z^2=x^2+2ixy-y^2 This is not equal to x^2+y^2. I'm confused.

Is there the possibility of "absolute time" Is there a theory of absolute time that is compatible with General Relativity? [SIZE="1"](This question inspired by a thread on http://www.freeratio.org/showthread.php?p=5740883#post5740883".)

What is "absolute reference pressure and absolute reference temperature" I am doinf a test about compressed air flow rate. There is a parameter called absolute reference pressure and absolute reference temperature. Are they 1.01bar and 273+20K?

Hi all, I'm currently preparing for pre-tertiary mathematics, studying from Apostol's "One-Variable Calculus". I have just begun to work on the theory of integration of trigonometric functions, but I found that with the last set of exercises (on finding area between two functions, over some...

Homework Statement In my latest experiment, I have found two sets of data from the data processing. Normally, the values in the data sets should be equal, but they are not as a result of the error of the experiment. How can I do the error analysis? (Percentage Error, absolute error...)...

Homework Statement Find: Lim | x2+x-12 |-8 / (x-4) x --> 4 Homework Equations The Attempt at a Solution My answer is 9. It it right ? or there is not a limit for F(x) when x --> 4

So, from what I've heard, absolute zero is 0 Kelvin, lowest temperature possible, -273.15 C, etc etc. Is it possible to even reach it? Why or why not?

Homework Statement \sum_{n = 2}^{\infty} \frac{1}{n*ln(n)} I have to find whether the series absolute converge, conditionally converge or diverge?2. The attempt at a solution I used the ratio test. so, lim(n to infinity) [n*ln(n)]/[(n+1)*ln(n+1)] since ln (n+1) will be...

Homework Statement Find the absolute minimum and maximum values of f on the set D. f(x,y)= e-x2-y2(x2+2y2); D is the disk x2+y2 <= 4 Homework Equations Second Derivatives test, partial derivatives The Attempt at a Solution fx(x,y) = 0 = (e-x2-y2)(-2x) + (x2+2y2)(-2x...

Homework Statement \int^{8}_{0}\left|x^{2} - 6x + 3\right|dx This is for a single variable AP Calculus AB class in which we are solving using substitution method. 2. The attempt at a solution I attempted it by just ignoring the abs value bars thinking that anything I am finding out...

Homework Statement Test the series for (a) absolute convergence, and (b) conditional convergence. \sum\left(-1\right)^{k+1}\frac{k^{k}}{k!} Homework Equations The Attempt at a Solution So I tried taking the absolute value and then applying the ratio test, which, after...

Does anyone have the equation that the absolute roughness is expressed in terms of Manning coefficient, with the reference included? I have found one from Webber 1971. n = k1/6/26 where: n = applicable Manning roughness coefficient, k = absolute roughness (mm) Reference :Webber...

Given an ideally isolated volume of a single species of gas that has reached internal equilibrium , would the individual molecules : [A] Retain the range of individual velocities and thermal energies [if present] and keep a merely statistically constant average...

this is the question, Prove that if f is continuous on (a,b] and if |f| is bounded on [a,b] then f is integrable on [a,b]. (note: it is not assumed that f is continuous at a.) I know you have to use the upper and lower bounds to prove this statement but i don't know where to start...

this is the question, Prove that if f is continuous on (a,b] and if |f| is bounded on [a,b] then f is integrable on [a,b]. (note: it is not assumed that f is continuous at a.) I know you have to use the upper and lower bounds to prove this statement but i don't know where to start? Thanks

Hey everyone. Just getting prepped for a midterm on Tuesday and looking for a bit of help on a few things. If there are any tricks to make some of this stuff easier that would be great. I remember there being a few from back in high school, but i can't remember them. I know the process for all...

Say we have an absolute sphere ball which is consist of an fully filled with air which the ball cannot expand anymore, as further pumping air will cause the ball explode. As a few air inside is leaked, the ball will not shrink since its membrane is inelastic, hence causing the ball to become a...

Homework Statement Find the Local and absolute extrema of f(x) on the interval [-1,2] and give a sketch of the graph if: f(x) = [ 1 / (1 + |x|) ] + [ 1 / (1 + |x - 1|) ] I am confused about the absolute value parts. I know they're the versions inside the absolute value signs when...

Homework Statement Show that following statement is true: If Σa_n diverges, then Σ|a_n| diverges as well. Homework Equations Comparison Test: If 0 ≤ a_n ≤ b_n for all n ≥ 1, and if Σa_n diverges, then Σb_n diverges as well. The Attempt at a Solution I tried to prove the...

Homework Statement I need to derive an error equation from the following equation... \frac{e}{m} = \frac{2V}{B^{2}R^{2}}Homework Equations Just... basic... derivation rules...The Attempt at a Solution I did try, just don't know how to put the stupid attempt in LaTeX... I'm stuck at the "2V"...

Hi, I was wondering if a function is absolutely convergent over a certain interval, say, (0,\infty) will its indefinite integral also be absolutely convergent over the same interval? Also, assume that f(x) is convergent for (0,\infty). Would g(x) = \int{\int_{0}^{\infty}f(x)dx}dy &=&...

Homework Statement Find the absolute max and absolute min values of function on the given interval: f(t) = 2cos(t) + sin(2t), [0,pi/2] Homework Equations The Attempt at a Solution f '(t) = 0 0 = -2sin(t) + 2cos(2t) 2sin(t) = 2cos(2t) stuck...

1. Evaluate \int_{-1}^{3} \left|x^2 -4\right| dx 3. The Attempt at a Solution This is the first time I'm trying this type of question & I think I need to use the following theorem for such questions; f is integrable on a closed interval a to b. \int_{a}^{b}f(x)dx =...

Homework Statement Find a number in the closed interval [1/2, 3/2] such that the sum of the number and its reciprocal is (a)as small as possible (b) as large as possible I am given the answer in the back of the book The answer to a is 1 The answer to be is 1/2 Homework...

Hi, according to 3rd law of thermodynamics, absolute 0 can never be attained. But i really don't understand how was the exact value of absolute 0 calculated almost 100 years back? I think it comes from the thermodynamic relationships, but i don't understand how. Can anyone explain me the...

Homework Statement I reduced a much harder problem to the following: Prove that if abs(a-b) is divisible by k, and if abs(b-c) is divisible by k, then abs(a-c) is divisible by k. Homework Equations none really. The Attempt at a Solution I tried setting abs(a-b)/k = n and abs(b-c)/k = m...

I'm taking an algebra & triginometry class at my college and my professor is kind of slow and unclear. I think I'm a fast learner and a good understander which is why I came here to get this info down. We're up to complex fractions or radical equations right now I think, forgot which. Something...

Homework Statement lxl <2 lx+2l The question is asking to solve this Homework Equations The Attempt at a Solution Ive tried bringint the 2 over which leads me to l-x-4l over lx +2l < 0 but then the absolute value confuses the heck out of me on where to go...

Today in my physics class we got into a discussion about Absolute Zero and gravity. The argument was that if Absolute Zero was achieved, would it still be affected by gravity? Because gravity is a force and would make whatever that was at Absolute Zero move, but to have motion there would be...

Prove the following: if |a| \leq b then -b \leq a \leq b (where b \geq 0 ). So a \leq b and -a \leq b . Then -b \leq a so that -b \leq a \leq b . Suppose that -b \leq a \leq b . Then a \leq b and -a \leq b so that |a| \leq b . Is this a correct proof? You don't have to...

Homework Statement Rewrite the following expressions without absolute value signs, treating various cases separately where neccesary Homework Equations a-Abs[(a-(abs)a)] the question is do i have 2 answers to this ?

Homework Statement Consider the function f:R^2->R defined by f(x,y)=[e^(x+y)]-y+x. Is there an absolute maximum value of f on the set s={(x,y):/x/+/y/<=2}? Justify. note, /x/ is the absolute value of x. Homework Equations a. If f is con't, it takes compact sets to compact sets...

Homework Statement F(x) = (8-12ln|x|)/(x^4) > 0 (a) For what values of x is the expression F(x) defined? Write your answer in interval notation. (b) At what value(s) of x is the expression F(x) equal to zero? If there is more than one answer separate them by commas. (c) The set of...

Homework Statement Question is: how can you tell if there are any places you can't take the derivative of an equation that has an absolute value (using logic, not just graphing it) example equations 1. \left|x-5\right| 2. \left| x3+4x2+9x+17 \right| x2+1 3...

Here, it says that for the limit f(x) = |x| / x, |x| = { x, x > 0 -x, x < 0 } What I don't undestand is why is |x| = -x for values under zero? Isn't the absolute value for negative values just x and not -x? thanks. EDIT: I don't want to start a new thread, but I got stuck on this...

Ok the problem is: lim x->-1 |x+1| / x2-1 (sorry i don't really know how to type the equation out) I think that you have to find the limit as x->-1 from both the left and right sides from right: so I got lim x->-1 = (x+1)/x2-1 = (x+1)/(x+1)(x-1) = 1/(x-1) =1/-1-1 =-1/2 How would I...

While reading my text, I came across an inequality that I couldn't convince myself of... For real numbers a,b: \left|a+b|<= |a|+|b|. Is this something proven? Or is it an axiom or something?

The graph of g is interm of f. So how to plot g(x)= f(|x|) and of g(x)=|f(x)|. Is it jus a 'V' shape one.This problem is in Spivak Textbook, Chapter 4. Thanks to all.:confused:

I have a question about something that has been bothering me for a while... In all of my chemistry classes, my professors have always told me that it is impossible to predict which way a chiral molecule will rotate plane-polarized light (i.e., you will see if a molecule is D or L, but, saying...

Homework Statement a. Find the value of x such as fx < gx where fx = |2x -1| and gx = x(2-x) b. evaluate \displaystyle\int^1_0 [gx - fx]\,dx Homework Equations none The Attempt at a Solution For question a I make it into 2 equation to 2x-1 = 2x-x^2 and 1 - 2x = 2x - x^2. I solve it and find...

Rigorous proof of basic "absolute value" theorem? Hey :) I'm working through a Real Analysis text, and I came across this theorem and "proof": http://img352.imageshack.us/img352/6725/proofbx2.png It kind of took me by surprise, because the author of the text is usually very careful about...

Homework Statement so this one says the sum of the series starting at n = 1 to inf. of ((-1)^n)arctan(n)/(n^2) Homework Equations Either a ratio test or just an abs. conv. test The Attempt at a Solution not sure how to play this one out, honestly. I see some semblance of hope...

Just wanted to say hi before I start my post! :smile: As you may know there is a property of the absolute value that states; for a, b \in R; |ab| = |a||b| Well, my friend asked me if I knew a proof for this... but I don't know... How can we prove this statement/property? I know there...

Homework Statement Find the absolute max and min values of f on the set D. f(x,y)=4xy^3 - (x^2)(y^2) - xy^3 D is the closed triangular region in the xy-plane with vertices (0,0) (0,6) and (6,0). The Attempt at a Solution I found my two critical points to be (1,2) and (2,0). Then I...

Homework Statement I am doing a project for which I am learning some aspects of electromagnetism by myself, so you can imagine how lost I am. Well, not completely: I was searching for a ferrite with high permeability as a core material. I learned how the octahedral and tetrahedral sites and the...

Ok this is something i learned few years ago and I am a bit rusty. So i have to find the absolute value of: \frac{1 - 2i}{3 + 4i} + \frac{i - 4}{6i - 8} So first i add the two fractions and i get: \frac{(1 - 2i)(6i - 8) + (i - 4)(3 + 4i)}{(3 + 4i)(6i - 8)} Next i simplify and then...

I've been told that as a person approaches the speed of light, time relative to others being viewed slows. when you make the speed of light ( if possible, I’m aware of distance change and mass increase and of the immense amount of energy needed to possibly reach this speed to push that mass)...

Hi folks - I'm struggling here! Please help ;-) Surely the concept of relativity of simultaneity is an illusion based on the finite speed of light? If an observer witnesses an event (Event A) and is at distance of zero (d=0) from Event A, then that is the TRUE time the event occurred. It is...