Interval Definition and 712 Threads

Homework Statement Problem 1 of 2: Why is it that the continuity of a function in a region R and the continuity of the first partial derivative on R enables us to say that not only does a solution exist on some interval I0, but it is the only solution satisfying y(x0) = y0? Problem 2 of...

Is there any general formula for interval bisection, rather than consider two similar triangles each time? Thanks

At any interval of space, is the net density of that interval never equal to zero?

Identify an interval [-a,a] so that |arctan(x)-x+x^3/3| < or = 10^-15 for all x E [-a,a]. Your result needs to be supported by a convincing proof I'm not sure how to go about this... can someone help me out? all i could probably do is... since.. 10^-15 is close to zero, i can find out...

Homework Statement A balls roll along a straight path with the following velocity and time intervals 3.0 s at +15.0 m/s 7.0 s at +20 m/s 6.0 s at -30 m/s 4.0 s at 3.5 m/s What is the displacement in the last 5.0-15.0 time interval: I've been looking at this question for a good 30...

Homework Statement Let I=[a,b] and let f:I->R be a function (not necessarily continuous) with the property that for every x in I, f is bounded in a neighborhood of x. Prove that f is bounded on IThe Attempt at a Solution I have no idea

Homework Statement Find an interval of length 1 that contains a root of the equation xe^{x}=1 Homework Equations The Attempt at a Solution I'm not quite sure how to find these intervals... Homework Statement Find an interval of length 1 that contains a root of the equation...

Craig Hogen, in his paper Indeterminacy of Holographic Quantum Geometry, Phys. Rev D 78, 087501 (2008), has claimed noise seen in output of the GEO600 interferometric gravitational-wave detector is evidence for a fundamental minimum interval time. What is the time-line for the survival of this...

Homework Statement Prove that the interval [0,1] is not a zero set. 2. The attempt at a solution Assume for contradiction that the interval [0,1] = Z is a zero set. This mean that given epsilon greater than 0, there is a countable coverage of Z by open intervals (ai, bi) (___I don't...

Can you just say that x(4-x) <4 for x \in (0,2) ? You don't need to prove this? Or to prove this, just find critical point which is x = 2 ?

I know that the diameter for an interval [a,b] is defined as b-a but what is 1. Diam of (-1,1]U(2,3) 2.Diam of (1,1/2)U(1/4,1/8)U(1/16,1/32)U... Thanks

Homework Statement Solve the following inequality and express the solution set in interval notation. http://www.webassign.net/www24/symImages/4/6/aaf987edafbf00c172f8cfaf01966c.gif The Attempt at a Solution I got most of the answer right, except the lower interval. the answer is...

Let's say we know this: \sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right) How do we get from this information to this expression of confidence interval for \theta? \left( \widehat{\theta} \pm...

Hello, I got the following problem; Find the min and max of the following function, on the following interval; f(x) = x^3 - 6x^2 + 9x + 15, [0, 5] Ok, to my knowledge, what I need to do is I: Find the first derivative and equal it to zero, so; f'(x) = 3x^2 - 12x + 9 0 = 3x^2 -...

A mountain climber stands at the top of a 59.4 m cliff that over hangs a pool of water. He throws 2 stones vertically downwards 1.77s apart and they cause a single splash. first stone initial velocity= -2.06m/s acceleration of gravity 9.8m/s^2 How long after release of first stone will the...

Hello in SR, the interval between two events is defined to be: s^2=x^2 + y^2 + z^2 - t^2 so my question is, why does the time get a minus sign? what differs it from the other 3 dimensions, what's the physical meaning of this difference and what is the physical meaning of this interval s^2...

Homework Statement Given the IVP problem \rm{(1+x^2)^{-1} \frac{dx}{dt} = \frac{\alpha \cdot 2 \pi}{4} \cdot cos(t)} \iff \rm{(1+x^2)^{-1} dx = \frac{\alpha \cdot 2 \pi}{4} \cdot cos(t)} dt Find the maximal solution with the initial conditio condition x(0) = 0. Then alpha is...

Homework Statement Find the interval of convergence of the infinite series: ∞ ∑ (x-1)n / 2n n = 1 Homework Equations Using the ration test. It converges if the absolute value of the limit of f(n+1)/f(n) as n -> ∞ < 1. Well, I hope that's how you write it. I'm...

I really ain't sure whether my problem is mathematical or related to Physics but i most probably think it has a mathematical solution. I am have a situation where I have subsurface seismic velocity windows at certain Depth points. In the window I have been given the two-way time in seconds...

I am trying to calculate the chi squared function for life data and a confidence level of 95%. I have 10 data points, a specified confidence level (95%), and 1 degree of freedom. I also have the alpha and beta parameters. Based on this information how can i calculate the chi squared statistic? I...

1. The problem: The function f is continuous for -3\leqc\leq5 and differentiable for -3<x<5. If f(-3)=6 and f(5)=-2, which of the following could be false? (a) there exists c, where -3\leqc\leq5, such that f(c)\geqf(x) for all on the closed interval -3\leqx\leq5. (b) There exists c, where...

What's the probability that a confidence interval (with alpha=10%), will have at least 85 of 100 predicted means within the calculated interval range (xbar +/- 1.645(sigma/sqrt(n)))? I understand that on average 90% of my means will be located in this range (and I know how to find this...

Homework Statement Finding the Radius of interval convergence of \sum n=1(theres a infinity on the sigma), "x^n/2^n" I really don't have a clue on which way I should go. Just a hint would be great:) Homework Equations The Attempt at a Solution

Homework Statement 1. Write an interval formula for the solution f'(x)=2f(x)+e^x f(1)=0 Explicitly find the maximal interval I about 0 on which we can solve the following differential equations 2. f'(x) = xf(x) f(0)=1 3. f'(x)=[f(x)]^2 f(0)=-1 Homework Equations For...

Homework Statement Let F(x) = \int^{x}_____________{0} x*e^(t^2) dt for x\in[0,1]. Find F''(x) for x\in(0,1). My only problem is the x, because the interval of the definite integral goes from 0 to x, and x is in the integral, even though the integral is with respect to dt. So I'd just like...

Lets say you have 5 trials, and 5 output let's say {5, 43, 60, 30 , 4}...so how would u get the chi sqaure from here & the confidence interval. i haven't work on prob &statc in years, thanks a lot for help folks

Lets say you have 5 trials, and 5 output let's say {5, 43, 60, 30 , 4}...so how would u get the chi sqaure from here & the confidence interval. i haven't work on prob &statc in years, thanks a lot for help folks

A container of oil is supposed to contain 1000 ml of oil. We want to be sure that the standard deviation of the oil container is less than 20 ml. We randomly select 10 cans of oil with a mean of 997 ml and a standard deviation of 32 ml. Using these sample construct a 95% confidence interval...

I need help with this question. Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let C.I = the width of the confidence interval for the average value y...

I am hopelessly confused on a homework assignment. The problem says " (a) Find the series radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?" Attached is a sample of problems from the book. Any help would be appreciated!

[SOLVED] Average Current Through A Coil Over An Interval Homework Statement The problem comes from a homework assignment I have. It has to deal with average current flowing through a wire over an interval. It is stated as follows: A five-turn circular coil of radius 15cm is oriented with its...

[SOLVED] Finding the Max Value of a Function on a closed interval Homework Statement Hi, I'm reposting this because it's a subsection to a larger question I had and I figured more people might be able to help with a new topic name. anyway i have the equation (eq1) C(t) = C + a(e^.5t) +...

Homework Statement A plane lands with a speed of 80.0 m/s and can accelerate with a maximum magnitude of 6.00 m/s^2 as it comes to rest. From the instant the plane touches the runway, what is the minimum time interval needed before it can come to rest? b. what is the minimum distance the...

[SOLVED] Sketching the Curves of a Function W/In an Interval - Simple (1st Year Calcu Homework Statement Sketch the graph of the function on the interval [0, 2pi]. y = cosx - 1/2(cos2x) Homework Equations The Attempt at a Solution so the problems that i have been practicing...

Homework Statement I am given the table \begin{array}{ccccc} samplesite & 1950 & 1975 & Change \\ 1 & 7.30 & 7.70 & 0.40\\ 2 & 6.14 & 6.72 & 0.58 \\ 3 & 6.47 & 6.32 & -0.15 \\4 & 5.87 & 6.38 & 0.51 \\ 5 & 6.06 & 6.34 & 0.28 \\ 6 & 4.71 & 5.78 & 1.07 \\ 7 & 5.45 & 5.59 & 0.14 \\ 8 & 6.17 &...

Graphing a function on a given interval...?? My problem is: Use a graphing calculator to graph the function...? ...over the given interval f(x)= -x^4+3x^3-4x+3 (-2,3). How do you graph something on a specific interval? P.S. I have the Casio fx-9750G PLUS graphing calculator.

Could someone pleases either: a. Justify the notion that the Lorentz interval between two events is independent of the observer, without referring to the Lorentz transformations. b. Derive the Lorentz transformations without resorting to the notion that the space-time interval between two...

Please tell me if it is possible to derive the formula which accounts for the Lorentz contraction from the invariance of the space-time interval. Thanks

Please tell me if the following statement is correct: In cc(dt)^2-(dx)^2=cc(dt')^2-(dx')^2 dx and dx' represent proper length dt and (dt') representing non-proper time intervals.

Don't understand why "an indefinite integral is valid only on a interval" Hi I'm using Stewart's Calculus, in the section of indefinite integral, they say: "Recall from Theorem 4.10.1 that the most general antiderivative on a given interval is obtained by adding a constant to a particular...

For summation from 1 to infinity of x^(n)/[2^(n)*n^(4)] - I get the radius is 2 by ration test, but how do I get the interval, just by pluggin in?

Hi, I am a stuck on figuring out how to get a 95% prediction confidence interval after I do a transformation. Here are some details. So we have some data on the brain weight and body weight of different mammals, and we are to perform linear regression on the data, predicting brain weight from...

Homework Statement Lets define a function f on an open interval ]0,1[ by setting f(x) = \int_{1/2}^\sqrt{x}} tln\frac{1+t^2}{1-t^2}dt Calculate the first three deriatives f'(x), f''(x) and f'''(x) Homework Equations Product and Quotent rule. The Attempt at a Solution...

Homework Statement the max value of f(x)=x^3(40-x^2) on the closed interval 0<= x <= 40 occurs at x=? The Attempt at a Solution different problem, same story (notes are unclear, and the book only complicates things more). I know the answer is 24, but this will not help me on the final exam...

Homework Statement The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the...

Hi everyone! I'm new here but I really hope you guys can be of some more help then my professor. We have our final exam next week (class ended today!) and the following 2 questions are on our review sheet. However, we NEVER covered this material. I'm terrible at "self taught" math so I'm having...

Homework Statement Find the radius and interval of convergence for the following power series. \sum_{n = 2}^{\infty}\frac {(1 + 2cos\frac {\pi n}{4})^n}{lnn}x^n The Attempt at a Solution R = \frac {1}{\lim_{n\rightarrow\infty}\sqrt [n]{\frac {(1 + 2cos\frac {\pi n}{4})^n}{lnn}}}...

The question asks to prove directly that the closed interval is covering compact - U= an open covering of the closed set [a,b] I started by taking C=the set of elements in the interval that finitely many members of U cover. Now I need to somehow use the least upper bound theorem to show...

[SOLVED] A Chebyshev interval with a poisson distribution Geophysicists determine the age of a zircon by counting the number of uranium fission tracks on a polished surface; the number of these uranium fission tracks on this surface follows a Possion distribution. A particular zircon is of...

The figure below shows a worker poling a boat-a very efficient mode of transportation-across a shallow lake. He pushes parallel to the length of the light pole, exerting on the bottom of the lake a force of 225 N. Assume the pole lies in the vertical plane containing the boat's keel. At one...