Absolute value Definition and 368 Threads

I'm given 1-a\cdot e^{-i\cdot 2 \pi f}. The squared absolute value apparently is |1-a\cdot e^{-i\cdot 2 \pi f}|^2=1+a^2-2acos(2 \pi f). Sadly the awnser doesn't show the steps of this derivation. I have tried many times to derive it my self but have not been able to do so. I feel like i...

Homework Statement lx/(x-2)l < 5 Homework Equations The Attempt at a Solution x/(x-2) < 5 x< 5x-10 10 < 4x 5/2 < x x/(x-2) > -5 x > -5x+10 6x > 10 x > 5/3 The answer is x < 5/3 and x > 5/2 so where did I go wrong on the second one?

Homework Statement $$\int_{0}^{\ 2\pi} \ |e^{sin(x)}cos(x)| \, dx$$ I know that it simplifies to $$ 2e- \frac{2}{e} ≈ 4.7 $$ I'm not sure how to approach this problem. Do I just break the integral up into the domains where it's positive and negative and integrate each component...

Calculate max and min point to function \frac{x^3}{2}-|1-4x| in the range \left(0,2 \right) I got one question, shall I ignore when it's \frac{x^3}{2}-(-1+4x) cause then x<0 and that don't fit in my range? Do I got correct?

Homework Statement Show that ∇_{x}|x-y|-3= -(x-y)|x-y|-3 x and y are vectors.Homework Equations The Attempt at a Solution When dealing with just a straight up absolute value I know that a solution can be found by using a piece wise approach, but I don't think that's what I should be using...

I want to calculate |e^{a^{2} + \frac{it}{m\hbar}}|^{2} i is imaginary unit. my trie: a^{2} + \frac{it}{2m\hbar} is a complex number so its module is: \sqrt{a^{4} + \frac{t^{2}}{m^{2}\hbar^{2}}} = \sqrt{a^{4}(1 + \frac{t^{2}}{m^{2}\hbar^{2}a^{4}})} a^2\sqrt{1 +...

Solve the system below: $\displaystyle |x+y|+|1-x|=6$ $\displaystyle |x+y+1|+|1-y|=4$ I've solved this problem and my intention is purely to gain another insights on how others would approach it and I surely hope you find this problem as an interesting one!:)

Homework Statement {(x1,x2)T| |x2|=|x2|} So my first thought is we would have to check for both cases (x1,x1) and (-x1,-x1) a=(x1,x1)T b=(v1,v1)T βa=(βx1,βx1)T for the case where a<0 βa(-βx1,-βx1)T thus it is closed under scalar multiplication. a+b=(x1+v1,x1+v1) for the case...

Homework Statement I need some help setting up this inequality: How accurate do the sides of a cube have to be measured if the volume of the cube has to be within 1% of 216 cm^3 Not very good with word problems and for some reason this course never deals with them until now? And this is...

I'm currently reviewing pre-calculus material and encountered a little problem with an absolute value expression. |3-x|=x-3 Now the way I learned absolute value expressions was that there's a positive and a negative case. So I got: 3-x=x-3 x=3 and -(3-x)=x-3 gives 0=0. Stupid question...

How find the limit of absolute value function? Hi everybody, I can't find the limit of (abs(x-2)-2)/x as x-->1. I know it's (-1) but I don't see how you get to it. If I take (x-2)>0 I get L=-3,(x-2)<0 I get L=-1. However according to the graph two sided limit does exist and it's (-1)...

f: R2 to R1 given by f(x,y) = x(|y|^(1/2)) show differentiable at (0,0) so I'm using the definition lim |h| ->0 (f((0,0) + 9(h1,h2)) - f(0,0) - Df(0,0) (h1,h2)) / |h| so first for the jacobian for f, when I'm doing the partial with respect to y, do I have to break this into the case y>0...

f: R2 to R1 given by f(x,y) = x(|y|^(1/2)) show differentiable at (0,0) so I'm using the definition lim |h| ->0 (f((0,0) + 9(h1,h2)) - f(0,0) - Df(0,0) (h1,h2)) / |h| so first for the jacobian for f, when I'm doing the partial with respect to y, do I have to break this into the case y>0...

Homework Statement If a,b,c and are all positive, and if |a-b| < c-b , then prove or find a counterexample to |a|<c Homework Equations The Attempt at a Solution So far I have been able to show |a-b|<c but don't know what to do next. THanks! BiP

Homework Statement Given: |x-a|<ε |y-b|<ε. proove: |xy-ab|<ε(|a|+|b|+ε) Homework Equations I need a direction for this proof. The Attempt at a Solution I tried by the info: -ε+a<x<ε+a and -ε+b<y<ε+b to ,multiply these inequalities, but it's not true. and i tried with the...

Which of the following two definitions is correct: 1) ##\forall x\forall y[ |x|=y\Longleftrightarrow( x\geq 0\Longrightarrow x=y)\wedge(x<0\Longrightarrow x=-y)]## 2) ##\forall x\forall y[ |x|=y\Longleftrightarrow( x\geq 0\Longrightarrow x=y)\vee(x<0\Longrightarrow x=-y)]## I think the...

Homework Statement we know that |a| < c and |bl < c prove that : (la+bl + la-bl)/2 < c The Attempt at a Solution all I've gotten to so far is this : la+bl < 2c lal + lbl < 2c we have : la+bl < lal+lbl then la+bl < 2c i need to prove that la-bl < 0.? also by squaring all i...

I need to find the derivative of y=| x | / squareroot of 2-x2. We never learned how to find the derivative with an absolute value, so I have absolutely no idea how to do this problem and I can't find an example in the textbook.

Homework Statement I need some help understanding an integral step in the example below. I get how the integrand was set up, but I don't get how comes to two expressions with the absolute value of z-L/2. (Problem description if that is needed: L is the length of a cylinder with radius R, and P...

Hi everyone,I have a problem.I get a short thermodynamics course.Until now,I have thought,that I know,what absolute value means. And here comes my problem.In lecture is writen,that if we want to make a synthesis in cell valid,we must to have:|ΔH|>|TΔS|.So what this expression means?Does it...

Homework Statement The absolute value of the gamma function \Gamma (x) that is defined on the negative real axis tends to zero as x \to - \infty . Right? But how do I prove it? Homework Equations The Attempt at a Solution I've tried to use Gauss's Formula...

I was hoping someone could give a little more insight, or perhaps enlighten me to a better way of approaching solving these seemingly simple Algebra 2 inequalities. I did some google searching but I was not able to find the answers I seek. The problem came up when a friend of mine had an...

The absolute value function f(x)=|x| has a global minimum at x=0. How could we prove this rigorously? In other words, how could we prove that there is no point c \ \epsilon \ ℝ such that f(c)<f(0) (Obviously, the function is not differentiable at x=0 so we cannot apply Fermat's...

Can someone check these ractice questions for me thanks.i need to understand what is being asked and how to go about this. 1.) For what values is it true that x is less than equal to |x| . 2.)For what values is it true that x=|x|?3.)|z|/-|z|,z is not equal to 0 4.)|t|/|t|, t is not equal to...

These i have tried to complete .someone please chech and correct them for me lease and thanks. can u give me steps when dealing with each one.like what i should do to attem these a)|-3-2| =|-5| =5 b)|-5|-|2| =-(-5)-2 c)|7|+|-4| =7+(-4)-7-4=3 d)|-11+1| |-10| =10 e)|6|-|-3| =6-(-3) 6-3=3...

I was thinking about identities, and seem to have arrived at a contradiction. I'm sure I'm missing something. A(n) (two-sided) identity for a binary operation must be unique. I will reproduce the familiar proof: Proof: Suppose a is an arbitrary element of a set S, e and e' are both...

Solve |x-3|^2 - 4|x-3|=12 The solution to this equation is -3, 9. But I'm not sure on the working. There is a hint to let u=|x-3| So I worked it out the following way. u^2 -4u = 12 u^2 -4u -12 = 0 (u + 2)(u - 6)=0 u /= -2 and u /= 6 |x-3|=-2 (no solution) |x-3|= 6, x = 9 Now to work...

I'm beginning self-study of real analysis based on 'Introductory Real Analysis' by Kolmogorov and Fomin. This is from section 5.2: 'Continuous mappings and homeomorphisms. Isometric Spaces', on page 45, Problem 1. This is my first post to these forums, but I'll try to get the latex right...

so I understand the basic premise of differentiating a first ODE, or I thought I did. I have the equation y'-y=abs(x-1). I have no idea of how to go about this. Can someone walk me through how to do this? I'm attempting to study for a test and this is one of the practice questions he gave us so...

Homework Statement [abs(x)]/[abs(x+2)]<2 Homework Equations The Attempt at a Solution case 1: [abs(x)]/[abs(x+2)]<2 case 2: [abs(x)]<2[abs(x+2)] is this right so far? if so, why is there two cases and what do i do next?

I was further looking into the Cauchy schwarz inequality and i got to a statement as follows: A·B ≤ |A·B| However, when I tried to prove this using numbers on paper, I wasn't sure if the absolute value bars distribute among each term, which would lead to |A|·|B|, or if the final product is...

Is this a correct a way of thinking for solving absolute value equations? Say I have |2x+6|-|x+3|=|x| and want to solve for x, then I have: For |2x+6| 2x + 6 if x ≥ -3 -2x - 6 if x < -3 For |x+3| x+3 if x ≥ -3 -x-3 if x<-3 For |x| x if x ≥ 0 -x if x < 0 Am I supposed to look at...

Just a general question with absolute values: Is it possible to have an absolute value of this form: | f(x) - L | < -L (the minus sign is meant to be there) and if so how can I convert it into expanded form? i.e: -L < f(x) - L < -L or something of that form.

Homework Statement ∫[|2x-1|] evaluated on the interval [1,-1] Homework Equations The Attempt at a Solution I know we must split it into two equations ∫ from [a,c] + ∫ from [c,b] and in absolute value one is negative and one is positive, so it will be 2x-1, and 1-2x my...

Homework Statement http://i.minus.com/i61zvy2BbtqkI.png Homework Equations One can factor the polynomial to (x-1)^2 The Attempt at a Solution After factoring the polynomial, I integrate (x-1) given the bounds of 0 and 1. I get -1/2. The solution manual says the answer is...

Homework Statement Given that \epsilon> 0, why is it, that \left | x_{n} -L\right |< \epsilon implicates that x_{n} > L-\epsilon ? Homework Equations The Attempt at a Solution

Homework Statement Minimize |2x1-3x2| subject to x1+x2≤5 -x1+x2≥-1 x1≥0, x2≥0 (a) Solve the problem graphically. (b) Formulate a linear program that could be used to solve the problem. Use software to solve your LP and show how to reconstruct a solution to the original problem...

Why does the half of the absolute value of a matrix formed with its coordinates give the area of a triangle? I don't see any similarity between that and the heron's formula.

For absolute value of x, f(x) = lxl To prove continuous, I can express it as a piecewise function of x if x>0 and -x if x<0 and then I can take the limit of each as x approaches 0 from the negative and positive sides. Both limits give zero, and f(0) gives zero, so continuity is...

Hello everyone, I'm posting here since I'm only having trouble with an intermediate step in proving that \sqrt{x} \text{ is uniformly continuous on } [0, \infty] . By definition, |x - x_0| < ε^2 \Longleftrightarrow -ε^2 < x - x_0 < ε^2 \Longleftrightarrow -ε^2 + x_0 < x < ε^2 + x_0 1...

Homework Statement Show that if bn→b, then the sequence of absolute values |bn| converges to |b|. Homework Equations The Attempt at a Solution I've been proving various properties of limits, including product of limits and sum of products, but have been having trouble making...

Write as one inequality with an absolute value x<-5 or 8<x not sure how you introduce the absolute value in this to solve it. thanks ahead

Homework Statement Suppose f is the function defined by f(x) = l x-1 l Sketch the graph of y = f(f(x)) Homework Equations The Attempt at a Solution It's not so much sketching the graph that is the problem as much as it is figuring out how to set up the equations. How do I put an...

I'm doing some practice problems, and with the help of my solutions manual and wolfram alpha I've worked out a solution to (x+1)\frac{dy}{dx} +xy = e^{-x} However, I don't understand why we can drop the absolute value bars when we calculate the integrating factor: e^{\int...

Suppose I want to compute tthe integral: \int_{-\infty}^{\infty}\frac{\textrm{sech}\hspace{0.1cm} x}{x^{2}-2|x|+1}dx Can I compute this integral via contour integration? The only way that I have thought of is to split up the domain: \int_{-\infty}^{\infty}\frac{\textrm{sech}\hspace{0.1cm}...

Let f(x) = |x|/x a. What is the limit of f, as x approaches 0 from the right? b. What is the limit of f, as x approaches 0 from the left? c. Hence, what is the limit of f, as x approaches 0? ------------------------------ The best way to evaluate limits involving absolute values is to use...

Dear Forum Users, I have got more math question rather then the physics question. Does someone know if: \mid d(x)\mid^2 equals just d(x), here d(x) is just the Dirac delta ? best regards, nykon

Homework Statement http://www4c.wolframalpha.com/Calculate/MSP/MSP621a026b7befdf1f1d00003b707661e1i20i4e?MSPStoreType=image/gif&s=55&w=126&h=38 Homework Equations limit x->3- (3x-9)/((abs(3x-9))The Attempt at a Solution I don't understand how to find the limit of absolute values..

Trig identity with natural logs and absolute value?? Homework Statement -ln|csc(x) + cot(x)|= ln|cscx(x)-cot(x)| Homework Equations The Attempt at a Solution I got that csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x), giving me a common denominator, added together I have...

Homework Statement Write f(x) = |x2-x-12| as a piecewise function. Homework Equations The Attempt at a Solution -x2+x+12 where x>1/2 x2-x-12 where x\geq0 According to the answer book the answers are -x2+x+12 where -3<x<4 x2-x-12 where x\geq4 2x2-5x-3, x\leq1/2 I am...