Absolute Definition and 1000 Threads

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 Draw the shear and moment diagrams for the loaded beam. Then answer the questions. The distance x is measured from point A to the right. I have attached an image of the problem. Homework Equations The Attempt at a Solution I've managed to answer...

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...

The question is: Show that if \suman from n=1 to ∞ converges absolutely, then \suman2 from n=1 to converges absolutely. I'm not sure which approach to take with this. I am thinking that since Ʃan converges absolutely, |an| can be either -an or an and for Ʃan2, an can be either negative or...

Homework Statement Find <x> in terms of X0 if X0 is constant and \Psi(x) = \frac{1}{\sqrt{X_0}}e^{\frac{-|x|}{X_0}} and <x> = \int^{\infty}_{-\infty}{\Psi^* x \Psi}dx where Psi* is the complex conjugate of Psi. Since there is no imaginary component, this is effectively Psi2. so, from...

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 Locate the absolute extrema of the given function on the indicated interval. f(x) = -x^2 + 3x ; interval: [0 , 3 ] Homework Equations The Attempt at a Solution f'(x) => -2x + 3x = 0 => x = 0 f(0) = -(0)^2 + 3(0) = 0 f(3) = -(3)^2 + 3(3) = 0 My answer: Absolute...

Hey guys, I was doing some homework and found something I don't quite understand. When calculating the absolute magnitude of the Full Moon, I came across a square root of its Albedo. (here - http://space.wikia.com/wiki/Absolute_magnitude). No idea why it's squared, but I can't get the +0,25...

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...

Homework Statement Find all real values of x that satisfy the following inequality. Homework Equations |x-3| > |x + 1| The Attempt at a Solution Splitting up the inequality into cases I get: 1. |x-3| > x + 1 and 2. |x-3| < -x - 1 1. x-3 > x + 1 or x-3 < -x - 1...

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...

Does anyone know how to calculate absolute uncertainty?? A student repeatedly measures the time taken by an object to cover a certain distance and obtains the following data: t1 = 2.432 s, t2 = 2.393 s, t3 = 2.402 s, t4 = 2.412 s, t5 = 2.424 s The instrument uncertainty is 0.001 s What...

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...

Solve: | |x+1| +2| - | x-2 | = 3 Relevant equations: if |x| = a, then x = a; x = -a My attempt: |x+1| +2 - (x-2) = 3 ; |x+1| + 2 - (x-2) = -3 (by theorem provided by teacher above) |x+1| = x- 1 ; |x+1| = x-7 if |x+1| < 0: -(x+1) = x -1 -x - 1 = x - 1 -2x = 0 x = 0...

Homework Statement Simplify. a) \sqrt{x^6} b) 8 \sqrt{x^7y^{10}} - 10 \sqrt{x^7y^{10}} For b, it's y^10. I can't make it look right for some reason. Mod note: Fixed the exponent. Homework Equations The Attempt at a Solution I can simplify all of them but I don't know when or where I need to...

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...

Prove the Schwarz's and the triangle inequalities for infinite sequences: If $$ \sum_{n = -\infty}^{\infty}|a_n|^2 < \infty\quad\text{and}\quad \sum_{n = -\infty}^{\infty}|b_n|^2 < \infty $$ then $\sum\limits_{n = -\infty}^{\infty} a_nb_n$ converges absolutely. To show this, wouldn't I need to...

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...

HeyI was wondering - is it physically impossible to make something absolute zero and then measure it to check if it was? I often read that we bring things down to "close to absolute zero" but it never is the full way. Is it because if human or electronic device, which ever it was that tried to...

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...

An experiment is performed to determine a physical quantity and 10 trials are made. The absolute uncertainty in the quantity can be given by a. the mean of the data b. the standard error of the data c. None of the above I'm leaning more towards b because absolute uncertainty has to deal with...

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...

what is the relation between Specific Heat and Absolute Temperature of any material ? Specifically, Sodium. Cp vs T ( not the change in temperature) Any mathematical formula ? Thanks

Hi, can you please give me some hints to show that \frac{|a-b|}{1+|a|+|b|} \leq \frac{|a-c|}{1+|a|+|c|}+\frac{|c-b|}{1+|c|+|b|}, \forall a, b, c \in \mathbb{R}. I tried to get this from |a-b| \leq |a-c|+|c-b|, \forall a, b, c \in \mathbb{R}, but I couldn't succeed. Thank you.

Homework Statement Solve Ix+3I>2 *I is used for absolute value notation The Attempt at a Solution Considering both a) Ix+3I > 0 then Ix+3I= x+3 b) Ix+3I < 0 then Ix+3I= -(x+3) when solved this would yield to; a) x>-3 and x>-1 b) x<-5 and x<-3 from my general reasoning i...

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...

Hello. I've been thinking about potential on charged capacitors, and got confused. A charge is AFAIK absolute - there is a balance of electrons and protons in matter, which can be biased one way or another. However, voltage is defined as difference of potential, not an absolute value. So...

I was wondering, since resistance decreases along with temperature for most metallic conductors (usually power function), in theory, if this conductor were to be at zero kelvin, would the resistance of this material also be precisely zero, or would it just be some extremely small value? If it...

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...

Hi Guys, I am trying to measure variability in a part for my sensor which l do not know the true value. So l decided that a good way to measure variability in this case would be to measure precision of my data points as l change this part on the sensor. So l was wondering, can l compare the...

Distribution of mass across the universe is not even. Therefore, passage of time should vary according to gravity. Which means at places time will pass at a higher pace or a lower pace than in respect of other places. Then, how is the entire Universe exactly 13.7 billion years old?

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...

I'm trying to calculate the luminosity of the sun in the infrared (J, H and K filters). According to http://mips.as.arizona.edu/~cnaw/sun.html, the absolute magnitudes of the Sun in each of these filters are J: 3.64 H: 3.32 K: 3.28. The absolute bolometric magnitude of the Sun is about...

Hello guys, I've been mulling over this thing for as long as I can remember. Since both time and space are relative in nature. Then what is absolute in this universe? Something must be. Because everything can't be relative, else what will they be relative to. Is it consciousness? If it is, then...

Hello! Is any covariant vector orthogonal to absolute derivative of its contravariant counterpart? I read a GR book, and it says the tangent vector of a curve is orthogonal to its absolute derivative, that is ##D\lambda^A/dst_A=0##, where ##t^A## is the unit tangent vector of some curve...

I'm trying to figure out why things happen to objects placed in environments near absolute zero. so let's take an ice cube. In a freezer it will remain stable, I'm guessing because the atoms that make up the ice cube will bounce off atoms in the air that are roughly similar in energy to the...

I took Calculus AB in my senior year of high school, but I had absolutely no idea what was going on since day 1. Of course, I failed the class. But now I'm in college and I have access to the internet at home now (I've never had internet at my home before this year) and I found all of these...

I want to treat this from a purely classical stance, ignoring all quantum and relativistic effects. If a body is undergoing centripetal acceleration, is the magnitude of the centripetal force absolute? If so, is its angular frequency also absolute?

Title says it all. I've been wondering. The argument is, is there a minimal temperature required for any chemical reaction to reach its activation threshold? Or would the energylessness of the atoms prevent bonds from forming (or dissolving, I guess)? Conrad.

Would it be possible to stand at a point, surrounded by sensors and fire beam of light of at specific frequency at every sensor and determine our absolute velocity without a reference based on the amount of red/blue shift detected in the frequency of each beam? Wouldn't light observed by the...

Law of Physic is not that absolute in the first place such as in place like event horizon. Assuming there is one, time travel does not use law of physics in the first place. It may use another set of law that is very obscure to us in current time, the Law of Time. Assuming there is Law of time...

I am new to the topic of special relativity. Having read a bit of Feynman and googling for answers I am still a bit lost. While I have an aptitude for logic, it does not extend quickly into physics or maths. So quite likely I am barking up the wrong tree and about to demonstrate my ignorance but...

Homework Statement ##\sum _{n=2}\dfrac {\left( -1\right) ^{n}} {\left( \ln n\right) ^{n}}##The Attempt at a Solution I have applied the Alternating Series test and it shows that it is convergent. However, I need to show that it's either absolute conv. or conditionally conv. Next, I tried the...

Homework Statement Determine whether the series is absolutely convergent, conditionally convergent, or divergent. ##\sum _{n=1}\left( -1\right) ^{n}\dfrac {n} {n^{2}+1}## the sum goes to infinity. Homework Equations Theorem for absolute convergence. Test for divergence The Attempt...

Homework Statement ##\sum _{n=1}^{\infty }\dfrac {\left( -3\right) ^{n}} {n^{3}}## According to Wolfram Alpha the series diverges by the Limit Comparison Test, but I remember that the limit comparison only works with series greater than zero. How is this possible? Homework Equations...

This is my first post, so forgive me if I'm posting in the wrong place or violating a rule. I've been doing some reading on relativity, and find myself flummoxed. I understand gravitational time dilation and the principals behind relative velocity time dilation, length contraction, and the...