intervals Definition and 288 Threads

1. A space vehicle accelerates uniformly from 85 m/s at t=0s to 462 m/s at t=10s. What is avg acceleration? How far did the space vehicle move from t=2s to t=6s. 2. Got the avg accel easily enough w basic equation for accel. Problem is conceptual with the displacement portion of the question...

Category of simple questions Obviously I am misunderstanding how an interval of space- time can be invariant under coordinate transformations. The following elementary (but obviously incorrect) calculation will illustrate my difficulty. Alice is leaving her two boyfriends, Bob and Charlie. Bob...

Mean Value Theorem Suppose that ##f## is a function that is continuous on ##[a,b]## and differentiable on ##(a,b)##. Then there is at least one ##c## in ##(a,b)## such that: $$f'(c) = \frac{f(b) - f(a)}{b - a}$$ My question is: wouldn't it be better to state that ##c## is in ##[a,b]## rather...

I want to make sure I understand how to deal with discontinuities when they lie within an interval of integration. Infinite Discontinuities In this case, do we always resort to improper integrals? Jump Discontinuities If there is a finite number of jump discontinuities in the integration...

Homework Statement Identify the intervals of increase/decrease of ##f(x) = \sin x + \cos x## Homework Equations ##f(x) = \sin x + \cos x## ##f'(x) = \cos x - \sin x = \sqrt 2 \cos(x+\frac {\pi}{4})## The Attempt at a Solution ##f## is increasing when ##f'(x) > 0## ##\sqrt 2 \cos(x+\frac...

Dear PF forum, Do anyone know, why music interval is always \sqrt[12]{2}?

Homework Statement Identify the open intervals on which the function ##f(x) = \cos \frac {x}{2}, 0 < x < 2 \pi## is increasing or decreasing. Homework Equations ##f(x) = \cos \frac {x}{2}## ##f'(x) = -\frac {1}{2} \sin \frac {x}{2}## The Attempt at a Solution I'm attempting to do these types...

Homework Statement [/B] Identify the open intervals on which the function ##f(x) = 12x-x^3## is increasing or decreasing Homework Equations [/B] ##f(x)=12x-x^3## ##\frac {df}{dx} = 12-3x^2 = -3(x^2 - 4)## The Attempt at a Solution [/B] I'm reading out of two textbooks. One is a...

Time-like and light like separations between events make sense, because a particle or a light flash can travel between them. However, how can you have a space-like interval when even light cannot travel such an interval (because its velocity is not greater than c). Obviously the first event...

Homework Statement 1.) When we collect more data for our confidence interval (A) Confidence Increases (B) Confidence Decreases (C) n decreases (D) The length of the interval decreases (E) The length of the interval increases 2.) We wish to determine a confidence interval for the population...

Homework Statement Find the intervals of increase/decrease. Use first derivative test to find the local maxima and minima. Sketch a rough graph. Homework Equations a) f(x) = 2x2+12x-1 b) f(x) = 1/2x4-2x2 c) f(x) = 3x-4 sqrt 2 d) f(x) = x2-1/x2+1 The Attempt at a Solution A) it becomes f...

Are there any charts (information) concerning the elements and Atomic Electron Transition intervals? Does each element have a time it takes from absorption to the time of re-emission? Concerning Spectral Lines are the result of interaction between a quantum system (atoms) and a single photon...

Hi everyone. Could anyone help me solve this. I need to find the increase and decrease intervals of f(x) = sin(-3x). The increase intervals of sin(x) are -\pi/2 + 2\pi*k < x < \pi/2 + 2\pi*k Is the following the right way to solve my problem (for increase intervals)? -\pi/2 + 2\pi*k < -3x <...

First of all, apologies as I've asked this question before a while ago, but I never felt the issue got resolved on that thread. Is it valid to prove that \int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx using the fundamental theorem of calculus (FTC)?! That is, would it be valid to do...

a study carried out to investigate the distribution of total braking time (reaction time plus accelerator to brake movement time in ms) during real driving conditions at 60 km/hr gave the following summary information on the distirbution of times ("A Field Study on Braking Responses During...

Is there an f(x) which is differentiable n times in a closed interval and (n+1) times in an open interval? I think I saw this in a paper related to Taylor's theorem (could be something else though). It didn't make sense to me, how can something be differentiable more in an interval that contains...

Hello! (Wave) Each two open intervals in $\mathbb{R}$ are equinumerous. It suffices to show that for each $a,b \in \mathbb{R}$ with $a<b$ it holds that $(0,1) \sim (a,b)$ $$f: (0,1) \xrightarrow[\text{surjective}]{\text{1-1}} (a,b)$$ $$f(t)=(1-t)a+b, t \in (0,1)$$ So this means for example...

I am reading Walter Rudin's book, Principles of Mathematical Analysis. Currently I am studying Chapter 2:"Basic Topology". Although I can basically follow it, I am concerned that I do not fully understand the proof of Theorem 2.38. Rudin, Theorem 2.38 reads as...

Hello guys! I´ve seen that for spacelike intervals, ie s^2 < 0 you´re able to swap the sign of s = x-y = y-x. Why is that? Thanks!

Homework Statement Hello, I'm not sure if it's the right place to post this exercise, but I'm learning it in a calculus course. I need to prove that: a) The complement of an open set is a closed. b) An open interval is a open set, a closed interval is a closed set. Homework Equations I have...

I've been watching the Khanacademy videos on Calculus and in this video, at 4:18: He talks about relative minima and maxima in an interval. He says that the relative extrema can't be at the endpoints. As far as I understand, in that case the interval would have to be an open one, but my...

Hello, I have to compute the numerical integral of a function which is expressed at unequal (but almost) intervals. I tried the trapezoidal method, but the error is too large for my application. Is it possible to generalize the Boole's rule to or something on the same order of precision?

As far as i understand, we (our mind) observe the universe at set periods of time, say, our consciousness activates each 0.5 seconds for instance. This means that we have no perception whatsoever of what happens between the 0.5 seconds that exist between our perceptions.This led me to the...

I know what it means by by even, or odd, function. i also know what it means graphically. My question is how to find a whether a function is even, or odd? if the function is defined in three intervals or more than three intervals. Consider a function F(x) defined in the interval (a,d) F(x)= [...

Hey guys, I'm having trouble with this problem set I'm working on at the moment. I'd appreciate some help with this question: This thread is only for question one. Please ignore number two. So I used the quotient rule to differentiate, giving me: f'(x) = [2x(x-2)-2(x^2)]/(x-2)^3...

Hey guys, Need some more help again. I'll keep it brief. This thread is only for question one. Please ignore 2ab. I started off by computing f'(x) via the product rule and calculating the zeros, at which point I got: x= 1/√ 5 and x=√(3) However, I'm at a loss as to what I should do...

Assumptions: f:[a,b]\to\mathbb{R} is some measurable function, and M is some constant. We assume that the function has the following property: [x,x']\subset [a,b]\quad\implies\quad |f(x')-f(x)|\leq M(x'-x) The claim: The function also has the property m^*(f([a,b]))\leq M(b-a) I'm not...

I am lost on how to do these two problems and can't find info on how to solve them anywhere. If anyone can get me on the right track as to how to start, that would be amazing! 1. A 99% confidence interval for a population mean was reported to be 152 to 158. If the standard deviation is 10...

I need some help find some continuous intervals for $f(x)=tan(2x)$. I know there are vertical asympotes when x=pi/4+2*pi*n for positive integers. Thank you for your help. CBarker1

Homework Statement Determine the intervals on which the function is continuous, support with graph. 15) f(x)=x^2+(5/x) 16) g(g)= 5-x, x<1 2x-3, x>1 17) f(x)=√(4/(x-8)) Homework Equations The Attempt at a Solution I understand the concept behind not...

Homework Statement #1: The graph of f' is shown. Find the intervals on which f increases. #2: The graph of f'(x) is shown. Give the interval(s) where the graph in concave down. Homework Equations Not sure. The Attempt at a Solution #1: Well, I thought it was (-infinity...

Recently I saw the results of an IQ test given with confidence intervals. While I know very well what a confidence interval is, I am not sure how you can give one for a psychological test. I think to determine a CI you either have to know the "true IQ" of an ensemble of persons and see how the...

Suppose I have a normally distributed random variable with unknown mean μ and known standard deviation σ. Based on n samples of the RV, I'd like to compute an estimate of μ and a confidence interval at confidence level P%. The usual way of doing this would be to use the standard error in the...

The problem states: I have 150 quarters. Calculate a confidence interval for the number of coins in my jar. The optimal change is always given. The distribution of coins are discrete uniform. I have also found that probability of a quarter=.31, probability of a penny=.42, probability of a...

Homework Statement A Gallup Poll of 1002 adults in October 2002 found that 25% of the respondents said that their household had experienced a crime in the past year. Among respondents aged 18-29 years, 43% had been victims of a crime. Gallup says, “For results based on the total sample of...

1. Homework Statement Suppose you receive calls that follow a Poisson process model Y(t). There are two hypotheses, Hypothesis1: E[Y(t)] = λ1t = 70t and Hypothesis 2: E[Y(t)] = λ2t = 75t. Let t = 30 the number of calls be 2175. Find and compute a significance level α such that both...

Homework Statement . Let ##\{I_n\}_{n \in \mathbb N}## be a sequence of closed nested intervals and for each ##n \in \mathbb N## let ##\alpha_n## be the length of ##I_n##. Prove that ##lim_{n \to \infty}\alpha_n## exists and prove that if ##L=lim_{n \to \infty}\alpha_n>0##, then ##\bigcap_{n...

Here's the question: The PCB concentration of a fis hcaught in Lake Michigan was measured by a technique that is known to result in an error of measurement that is normally distributed with a standard deviation of .08 ppm. Suppose the results of 10 independent measurements of this fish are...

I have a simple question about special relativity time intervals. Say when the origins of 2 frames are colocated, they sync their clocks to 0. At time t1, frame 1 emits a light pulse. Then at time t2>t1 frame 1 emits a second light pulse. That is a time interval I in frame 1. In frame...

Homework Statement Prove whether f(x) = x^3 is uniformly continuous on [-1,2) Homework Equations The Attempt at a Solution I used Lipschitz continuity. f has a bounded derivative on that interval, thus it implies f is uniformly continuous on that interval. But as it is not a...

Homework Statement Problem 2: Find the absolute extreme values of f(x) on the interval (1, infinity). Homework Equations The Attempt at a Solution It seems as if this is an indiscretion by the teacher. Absolute extrema don't occur on open intervals except in the case of (-∞,∞) such as in...

Homework Statement Suppose that a continuous function f(x) has horizontal tangent lines at x = -1, x = 0, and x = 1. If f"(x) = 60x^3 - 30x, then which of the following statements is/are true? A) f(x) has a local max at x = 1 B) f(x) has a local min at x = -1 C) f(x) has an inflection...

Express the set {X E R: (x+3) (7-x) ((x-2)^2) > 0} as a union of intervals

in creating a list of numbers to find mean, median, mode, range and some other questions with this table height in meters| frequency 8 \le h < 10\ \ \ \ \ \ \ \ \ \ 6 10 \le h < 12\ \ \ \ \ \ \ \ 5 12 \le h < 14\ \ \ \ \ \ \ \ 7 14 \le h < 16\ \ \ \ \ \ \ \ 4...

Is there a formula or something? When I solve quadratic equation I get two roots of x1 and x2. how can I find out the length? Thank you

Homework Statement Given that f(x)= x* ((ln x)^2) f'(x)= ((ln x)^2) + 2 ln x f"(x)= (2 ln x) (1/x)+ (2/x) (a) find the intervals on which f(x) is increasing. (b) find the intervals on which f(x) is concave up. (c) find lim f(x) as x-> +∞ and lim f(x) as x -> 0+ Homework Equations The Attempt...

In a rigorous mathematical course I am talking, it seems to make a difference when I am given a function f and need to write its Fourier series, whether it is defined on [0,2∏] or [0,2∏). What difference does it make for my series whether it is an open or a closed interval?

Homework Statement For the function f(x) = x^3 - x^2 + 4x - 3 Homework Equations The Attempt at a Solution I found the first and second derivative, the first derivative is f'(x) = 3x^2 - 2x + 4 This is not factorable, as the discriminant is < 0, meaning there is no...

Hi I have a certain experiment that I repeat 40 times and get the result: 0.001 +/- 0.004. Now I've repeated the experiment using a different method (so it is essentially a new experiment) and I get a new value: -0.002 +/- 0.003 Now, is it true to say there is no statistically...

Homework Statement We have C_n = [1-\frac{1}{n},2-\frac{1}{2n}] and C = C_1 \cup C_2 \cup C_3 \cup ... and are asked to describe the interval C and then prove that it is actually what we say it is. Homework Equations The Attempt at a Solution I am guessing that C = [0,2) and...