Value Definition and 1000 Threads

I am reading Manfred Stoll's Book: "Introduction to Real Analysis" ... and am currently focused on Chapteer 4: Limits and Continuity ... I need some help with an inequality involving absolute values in Example 4.1.2 (a) ... Example 4.1.2 (a) ... reads as follows:In the above text we read ...

Homework Statement If ##P(x)\propto e^{x^2/2\sigma^2}##, show that the average ##\langle x^2\rangle = \sigma^2##. Homework Equations ##\langle x\rangle = \frac {\int xP(x) \, dx} {\int P(x) \, dx}## The Attempt at a Solution ##I = \int x^2e^{x^2/2\sigma^2} \, dx = \int (-\sigma^2x)(\frac...

Homework Statement Prove that A(X(ωk)2)≥A(X(ωk))2 if and only if X(ωk) has the same value for every k such that pk>0 for every category which actually occurs in the population Homework Equations A(X)=1/N∑nkX(ωk)=∑pkX(ωk) The Attempt at a Solution A[(X-A(X)2)]=A(X2)-A(X)2 and i believe the...

Homework Statement ## y''+\lambda y = 0 ; y(0) = 0, y(\pi)-y'(\pi) = 0## Homework EquationsThe Attempt at a Solution So, we have to test when lambda is equal to, less than and greater than 0. Let ## \lambda = 0## thus, the ODE becomes ## y'' = 0 ## which implies solutions of the form ## y(t) =...

If $x_1,x_2,...,x_{2017} \in\Bbb{R}_+$ and $\frac{1}{1+x_1}+\frac{1}{1+x_2}+...+\frac{1}{1+x_{2017}} = 1$ - then find the minimal possible value of the expression: \[\prod_{i=1}^{2017}x_i\]

Homework Statement Find the eigenvalues and eigenfunctions of the following boundary-value problem. ## y''+\lambda y = 0 ; y(0) = 0, y'(L) = 0 ## Homework EquationsThe Attempt at a Solution So, we have to test when lambda is equal to, less than and greater than 0. Let ## \lambda = 0## thus...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] I don't understand how can current in ammeter be zero .Why is 2V battery not sending current in the right loop ?

I'm getting a bit confused by the specific notation in the question and am unsure what exactly it is asking here/how to proceed. Homework Statement Given a scalar function ##f## find (a) ##∫f \vec {dl}## and (b) ##∫fdl## along a straight line from ##(0, 0, 0)## to ##(1, 1, 0)##.Homework...

Find the minimal value of the expression $\frac{a}{b}$ over all triples $(a, b, c)$ of positive integers satisfying $|a^c − b!| ≤ b$.

In a paper from 2003, it has been shown that the particle horizon is about 14300 Mpc, or 46.6 billion light years (and it has been recalculated in 2016 with more accurate parameters values at around 14200 Mpc = 46.3 billion ly). From what I understand, the calculation proposed in 2003 takes the...

Homework Statement Ans: c) Homework EquationsThe Attempt at a Solution I can solve this problem if only I understand the setup . I am sure the diagram is missing something . Can someone help me understand the problem statement in context of the setup ?

In uniform circular motion, direction of particle is changing at every moment but its speed remains the same. If the magnitude of velocity or speed remains the same, change in magnitude of velocity is zero. Then how come radial acceleration can have a calculated value since acceleration = change...

Consider a continuous function f in [a,b] and f(a) < f(b). Suppose that \forall s \neq t in [a,b], f(s) \neq f(t). Proof that f is strictly increasing function in [a,b]. Homework Equations I.V.T: If f is continuous in [a,b] and \gamma is a real in [f(a),f(b)], then there'll be at least one c...

I have a statistics problem that is probably not too difficult for someone who knows what they are doing, but I still need help with it. Here’s the scenario. There is a town with a highway built at the end of 2013. The mayor is concerned because of the number of traffic accidents on the...

Homework Statement Homework Equations f ' (x) = 0 --> to find extreme points The Attempt at a Solution ## 2x^2 + y^2 = 4## ## y = \sqrt{4 - 2x^2}## ## y ' = \frac {-2x} {\sqrt{4-2x^2}} ## ## 0 = \frac {-2x} {\sqrt{4-2x^2}} ## x = 0 also ## 4 - 2x^2 >= 0 ## ## 4 >= 2x^2 ## ## \sqrt{2} >= x...

Homework Statement Homework Equations f ' (x) = 0 -> to find extreme pointThe Attempt at a Solution can I differentiate the function directly? f ' (x) = |1| + | 2x - 2| 0 = 2x - 1 x = 1/2 and x from domain = { 0, 2 } the range we get : f(0) = 1 f(2) = 1 f(1/2) = 1/2 + 3/4 = 5/4 min = 1 max...

Homework Statement Imagine you are playing a game with me, of drawing balls from a box. There are two blue balls and two red balls. They are picked with equal probability, and are drawn without replacement. If you draw a blue ball, I give you $1. If you draw a red ball, you pay me $1.25. What...

Homework Statement Homework Equations polynomial equation $$(a+b)^2 = \sum_{k=0}^{n} \binom nk a^{n-k} b^k $$ The Attempt at a Solution i get $$ \frac {1} {32} + \frac {5} {16}\frac {3^{0.5}i} {2} +\frac {10} {8}\frac {3i^2} {4} + \frac {10} {4}\frac {3^{1.5}i^3} {8} + \frac {5} {2} \frac...

Rewrite each statement using absolute values. 1. The number y is less than one unit from the number t. y < | t - 1 | 2. The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin. | a + b - 0 | > or = | a + b - 0 | Is this correct...

Rewrite each statement using absolute values. 1. The distance between x and 4 is at least 8. | x - 4 | > or = 8 Can this also be expressed as | 4 - x | > or = 8? If so, why? 2. The distance between x^3 and -1 is at most 0.001. | x^3 -(-1) | < or = 0.001 Can this also be expressed as | - 1...

The | x | = x when x > or = 0. The | x | = - x when x < 0. Rewrite the following expression in a form that does not contain absolute value. | x + 3 | + 4 | x + 3 |, where x < -3 -(x + 3) + 4 -(x + 3) -x - 3 + 4 - x - 3 -2x - 6 + 4 -2x - 2 Correct?

Hello, I have a problem which I did solve, but I ain't sure of something in it, something small to be honest. The question is: Use a binary search and the function f(x)=x^2-5 in the domain [2,3] to find approximation for the value of the square root of 5, with an accuracy of 1/16. What I...

In 1D QM: I understand that if a given potential well, U(x), is symmetric about x = L, then the expectation value for operator [x] would be <x> = L. (I am not even entirely sure why this is, guessing that the region where x<L and x>L are equally probable) Is it possible to draw conclusion...

Homework Statement galvanometer with 50 divisions on the scale requires a current sensitivity of 0.1 m A/division. The resistance of the galvanometer is 40Ω. If a shunt resistance 0.1 Ω is connected across it, find the maximum value of the current that can be measured using this ammeter...

Hello, I am calculating pressure drop through a pipe using CFD, which will be validated with hand calculations and experiments for a project. When I take results from my software, I can either take the pressure at a specific point (assume the centreline of the pipe) or I can take an average...

Homework Statement A block of mass 7 kg is pushed against a wall by force P. The coefficient of static friction between the block and the wall is 0.42. Determine an expression for the force P as a function of θ such that the block will not slide up the wall or fall down the wall. a.) Draw a...

You are given an equation and a point. In each case, find the value of the constant a so that the graph of the equation passes through the given point. y = -5x - a; (-4, 1) Solution: Let x = -4 and y = 1 y = -5x - a 1 = -5(-4) - a 1 = 20 - a 1 - 20 = - a -19 = -a -19/-1 = a 19 = a...

Homework Statement Homework EquationsThe Attempt at a Solution i just straight up applied am gm ##\frac {x}{y+z} + \frac{y}{x+z} + \frac{z}{x+y} \geq 3(\sqrt[3]{\frac{1}{(y+z)(x+z)(x+y)}}) ## so the denominator is which i had to maximise ## x^2(y+z) + y^2(x+z) +z^2(x + y) + 2\\...

Rewrite each statement using absolute values. 1. The distance between x and 4 is at least 8. Work: | x - 4 | > or = 8 Correct? Why must we write greater than or equal to for AT LEAST statements? 2. The distance between x^3 and -1 is at most 0.001. Work: | x^3 - (-1) | < or = 0.001...

Homework Statement Given that a1+a2+a3+... +a7=1 and that all aj is smaller than 1 and greater than 0 and variable , find the maximum value of 6a1+5a2+4a3+...+ a6 Homework Equations no further constraints The Attempt at a Solution I have no idea how to solve this problem specifically, but I...

Homework Statement A small generator of 5kW, 240V and a constant frequency is used to light up 35 bulbs in parallel, each one has (240 V, 60 W) printed on it. Calculate the resistance of each light bulb. Homework EquationsThe Attempt at a Solution Attempt 1[/B] Pw = V²/R ----> R = V²/Pw...

Hi, I'm stuck on a problem. I have this function that represents the velocity: f(v)=v2e(-mv2)/(2kT) T is the temperature and equals 293.15K m = 4.65 .10-26 kg k = 1.38 .10-23 J/K The problem wants us to find the derivative of the function. I found: df/dv= (2v)...

Homework Statement Hello! Please, help me to learn how to solve the following task - I really have no idea how to do that. What's important is that I need an algorithm that I can apply to the equation with different values. Homework Equations The initial equation: (y - z + i) mod m = x - z...

The square of X is equal to 4 times the square of Y. If X is one more than twice Y, what is the value of X?

$\triangle ABC ,if \,\, \angle BAC=\angle ACB=50^o$ point $M$ is an inner point of $\triangle ABC ,$ given :$\angle MAC=10^o$ and $\angle MCA=30^o$ find the value of $\angle BMC=?$

During a labexercise we measured a value to be 26.3 mT. The teslameter was said to have an accuracy at +- 0.05%. This means we measured 26.3 +- 0.0132mT. However we are supposed to write a measured value with it's error in the last digit. But the error is smaller than the smallest digit we got...

Hello, I'm a student of electrical engineering. This task appeared in one of the past exams. I've been using the procedure I believe should yield the correct result, however, it turns out I was wrong. Could somebody please check out where the mistake lays in my calculations? Homework Statement...

In order to calculate the energy of a reaction's ejectile, we make use of the concepts of the conservation of energy and momentum along with the reaction Q energy. However, if there is a threshold energy with above zero, meaning Q value is negative, do we have to consider the threshold energy as...

Precalculus by David Cohen 3rd Edition Chapter 1, Section 1.2. Question 68, page 11. Before typing the textbook question, I must say that I have not been able to find a satisfactory answer to absolute value equations that equal a negative number. Question: Explain why there are no real...

Homework Statement Homework EquationsThe Attempt at a Solution I don't know how to calculate part C) of the question. I'm unsure what saturation of a transistor refers too.

i showed that an 2 = a02 if n is even and 1 - ao2 if n is even how am i supposed to evaluate this at infinity

Homework Statement At t=0, the system is in the state . What is the expectation value of the energy at t=0? I'm not sure if this is straight forward scalar multiplication, surprised if it was, but we didn't cover this in class really, just glossed through it. If someone could walk me through...

We were given an experiment in which the %age uncertainty of majority of students happened to be greater than 100?

Is there a value for the acceleration of light? I tried to use a = v2-v02/2(x-x0) but then I just knew that light has no initial velocity so it can't be 0.

Prove that if f is a differentiable function on R such that f(1) = 1, f(2) = 3, f(3) = 3. There is a c \in (1 , 3) such that f'(c) = 0.5 I think the mean value theorem should be used, but I can't figure out how to prove such value exists

Homework Statement Hi guys, I am going to calculate the following integral: $$\int_0^{f_c+f_m} |Y(f)|^2\, df$$ where:$$Y(f)=\frac{\pi}{2} \alpha_m \sum_{l=1}^{L} \sqrt{g_l}\left [ e^{-j(\omega \tau_l - \theta_m)} \delta(\omega - \omega_0) + e^{-j(\omega \tau_l + \theta_m)} \delta(\omega +...

What is the value of K? K(x^{6}) = 1

Homework Statement Hello all, I created a predictive model from a data set of observed values and am looking for probabilities for accuracy. Data set A (observed) and data set B (predictive model) have a correlation of 84 % using linear regression. Data set A and B are both normally...

Hello. I was having a hard time determining how the formula for the average value of the waveform can be achieved. I've read that the ave since the waveform is symmetric is (Imin+Imax)/2. I want to know how to derive it using calculus. Thanks.

Homework Statement Using these two prototypes, double minValue( const double a[], unsigned els); double minIndex(const double a[], unsigned els); I am supposed to find the smallest value of an array using the minValue function as well as it's index by using the separate minIndex function and...