intervals Definition and 276 Threads

Homework Statement Prove a simple formula for the number of closed intervals with integer endpoints contained in the interval [1,n] (including one point intervals), where n is a natural number. The Attempt at a Solution I know that the formula ends up being the sum of i from i=1 to i=n...

I was trying to prove that the sigma algebra generated by the set of open intervals is the same as the sigma algebra generated by the set of open sets. This proof devolves into proving the statement in the title. I think rational numbers must be brought into the picture to prove this stmt but I...

In general, if f(x)=k but only for a < x < b and c < x < d how would you integrate the graph ? To find the mean for example, would you find the mean for each and add together, or is there some special thing for this case?

Homework Statement I'm trying to do problem #5 on this worksheet http://ugnotesonline.com/attachments/008_t1.5pst.pdf Homework Equations none The Attempt at a Solution (a) I tried to take the derivitive of the function in the intergral so I could see where it was increasing and...

Homework Statement Gravity on a falling object causes the object to descend a distance of d=4.9t^2, where d is the distance in meters and t is the time in seconds. A bowling bll is dropped from the top of the Eiffel Tower in Paris, France, which is 324 meters in height. If you neglect any...

Homework Statement Consider the function below. (Round the answers to two decimal places. If you need to use - or , enter -INFINITY or INFINITY.) f(θ) = 2cos(θ) + (cos (θ))^2 0 ≤ θ ≤ 2π (a) Find the interval of increase. ( , ) Find the interval of decrease. ( , ) (b) Find the local...

Problem: We define half infinite intervals as follows: (a, \infty) = {x\in R | x>a}; [a, \infty) = {x\in R | x\geqa}; Prove that: (i) (a, \infty) \subseteq [b, \infty) \Leftrightarrow a\geqb, (ii) [a, \infty) \subseteq (b, \infty) \Leftrightarrow a>b. I've got pretty much no idea how...

Homework Statement Prove that any open subset of \Real can be written as an at most countable union of disjoint open intervals. Homework Equations An at most countable set is either finite or infinitely countable. The Attempt at a Solution It seems very intuitive but I am at lost...

Let b be a real number. Correct me if I'm wrong, but it seems that: (1) The interval (b,b) is empty, as are the intervals (b,b] and [b,b). (2) The interval [b,b] consists of a single point (namely, b).

Homework Statement The Tale: The Klingon home world of Kronos is located at x=0. At time ct=-4 , a wonderful event occurs: Federation emissaries negotiate a peace treatywith the Klingons, bringing many years of warfare to an end! As part of this treaty, the Federation agrees to share its vast...

Homework Statement Let f be the function defined by f(x) = xe^{1-x} for all real numbers x. a. Find each interval on which f is increasing. b. Find the range of F. c. Find the x-coordinate of each point of inflection of the graph of f Homework Equations I don't think there...

Homework Statement \int^{1/\sqrt{2}}_{0} \stackrel{arcsinx}{\sqrt{1-x^2}}Homework Equations The 0 is supposed to be on the bottom of the intergal, but I could not format it to go there. The Attempt at a Solution My attempt was to set u= arcsinx, then DU would equal the bottom, so it would be...

Homework Statement I had a question about intervals and their reciprocals. If you have the reciprocal I where I is [r,s] than the reciprocal is [1/s , 1/r]. My question is when an interval contains zero, does the interval have a reciprocal. For instance if J is the interval [-2,7] does J have...

An arrow is shoot up in the air at 50m/s. Its height in meters after t sec. is h=50t-0.36t^2. Find the average velocity over interval [1,1.03], four decimal places.

Homework Statement Give an example of a power series tha converges on the interval (3,6), but on no larger interval. Give some justification. Homework Equations The equation needed is probably that for a power series: \Sigma cn(x-a)n The Attempt at a Solution I'm not sure at all. The...

Homework Statement Suppose the porosity (in %) of samples taken from the ground found to be normally distributed with σ = 0.85 % What sample size is necessary to estimate the true mean porosity to within 0.25 with 99% confidence? Homework Equations C.I. = confidence interval =...

Hey ladies and gents, I have a question that I'm not fully getting. An FL Student Survey reprts the results for responses on the number of times a week the subject reads a newspaper: Variable : news n = 60 mean = 4.1 standard deviation = 3.0 SE mean = 0.387 95% CI = (3.325-4.875)...

Homework Statement Let [a,b] be an interval and let A be a subset of [a,b] and suppose that A is an infinite set. Suppose that A is uncountable. Prove that there exists a point z which is an element of [a,b] such that A intersect I is uncountable for every open interval I that contains...

Homework Statement The amount of water in a storage tank, in gallons, is modeled by a continuous function on the time interval 0<=t<=7, where t is measured in hours. In this model, rates are give as: (i)The rate at which water enters the tank is f(t)=100t^2*sin(sqrt(t)) (ii) The rate at...

[b]1. Polotical parties rely heavily upon polling to measure their supports in the electorate. Below are the results of a poll conducted in 1996 for four (i only listed the one needed) political parties. Level Count Probability Stderr Prob N 250...

Prtesent the Lorentz transformations as dx=g(dx'+Vdt') dt=g(dx-Vdt) In my oppinion dx and dx' represent proper lengths measured in I and in I', dt and dt' representing coordinate time intervals. Do you aggree. Happy new year to all participamts on the Forum

Homework Statement y" +4y = g(x) ; y (0) = 1 & y(0) = 2 g(x) = sinx , 0 \leqx \leq pi/2 0 , x \succ pi/2 Homework Equations The Attempt at a Solution 1> g(x) = sin x solving i get : yc = ec1sin2x + ec2cos2x US set of sin x = {sinx...

Homework Statement Prove the intervals of real numbers (1,3) and (5,15) have the same cardinality by finding an appropriate bijective function of f:(1,3) ->(5,15) and verifying it is 1-1 and onto Homework Equations I know there are multiple ways to prove one to one and onto I am not sure...

I was under the impression that 95% C.I requires that the critical value in the error term comes from a t-distribution with 25 degrees of freedom. I was taught in class today that a 25% CI requires that the critical value in the error term comes from a t-distribution with 23 degrees of...

Homework Statement f:(0,1]->R be a continuous function. Is it possible that f does not have an absolute min or max. Give counter examples Homework Equations The Attempt at a Solution Since f is partially bounded, if I break the interval down into smaller sub intervals, each will...

i would like someone to clear my doubts by explaining how it actually works..limits is one of the chapter i fear about it cause I am quite blur with it..so i do need someone help me;v this que..given f(x)=1/x^3 what r the intervals for function continuous ?how to solve it?thanks :)

I have y_{ij} = \mu_{i} + \alpha x_{ij} + e_{ij} where i = 1, 2,3 and j = 1, \ldots , r . \mu_{i} represents the mean of the data set plus factor levels i , \alpha x_{ij} is a continuous variable. So, the problem is the following: Construct confidence intervals for \mu_1...

Homework Statement let g(x)=2x^5-10x^3=15x-3. find the intervals on which G is increasing and decreasing. and find the intervals of concavity and the inflection points Homework Equations The Attempt at a Solution i know how to find the increasing and decreasing intervals. i just...

My textbook says the following: For a closed interval J_n = [a_n, b_n] "A nested sequence of rational intervals give rise to a separation of all rational numbers into three classes (A so-called Dedekind Cut). The first class consists of the rational numbers r lying to the left of the...

Homework Statement Prove the any bounded open subset of R is the union of disjoint open intervals. The attempt at a solution I've seen a proof of this using equivalence classes, which is fine, but I want an unsophisticated solution, e.g. one relying on just the definitions of "bounded"...

Homework Statement Prove that the union of intervals [1,n] from n=1 to n=infinity is all of N. The Attempt at a Solution Do I use induction on this? Archimedes? (This question is before the section of Archimedes though). I need help on how to start it!

Am I correct in thinking that the union of disjoint open sets cannot span a continuous interval? Assume that each of the sets is a proper subset of the interval. Does this apply even if the collection of open sets is uncountable infinite?

I guess I've fallen through some of the cracks in the plethora of definitions I've learned, or I just never had enough examples of taking limits of intervals. Anyways, which is true, and why? $\cap^{\infty}_{n=1}(0,\frac{1}{2^{n-1}}]=0?$...

The problem in question is as follows: Find themargin of error for the given values of c, s, and n. where c is the confidence interval, s is the sample standard deviation and n is the number of objects. c=0.65 s= 1.5 n=50 the formula: E= (zc s) / n^.5 Level of Confidence Chart...

So if the interval between two events is spacelike, does that mean that the two events cannot effect each other? Does that also mean that no observer can observe both events?

Homework Statement An uncharged 1.15 uF capacitor is in series, through a switch, with a 4.50-M Ohms resistor and a 24.0- V battery (with negligible internal resistance.) The switch is closed at t = 0 and a current of Ii immediately appears. (Which I calculated to be 5.33 uA.) How long will...

we need to show with 90% confidence that the probability of the "treshhold number" being correct is 99.99%. "So we want P=0.9999 with C=0.90". we can consider 5 trails without put { 4, 7, 12, 9, 11}..we can say the treshhold # is the "2nd trail = 7"... i tried doing it using t alpha but i failed...

Does anyone know how to find exact confidence intervals? I've looked through textbooks, but they only find approximate CIs using the assumption that \frac{\hat{\theta}-\theta}{se(\hat\theta)}}\rightarrow Z. So given a estimator, \hat\theta do I have to find an exact distrubution for the above...

Hi everyone, Trying to revise and I came across this question: Solve the eqn cosec^2x = (3cotx + 4)/2, giving all values of x in the interval 0 < x < 2pi in radians to two dp. I ended up with two principal values/angles (working in degrees at the moment), which are: tan^-1(x) =...

I've recently been looked a little more into the ergoregion and the static limit of a rotating black hole and would appreciate any feedback regarding the question below in respect of the transition of time-like to space-like intervals at the static limit. The Killing vector field* for a...

ok. So if the second derivative of a function is equal to a constant and i want to find any intervals of concavity there is none right? therefore no infelction points nor relative and/or absolute extrma f(second derivative)(x)=2

I have a prescription for Wellbutrin, a drug which blocks reuptake of dopamine (strong) and noradrenaline (weak). I got this prescription because my family wasn't keen on my idea of self-medicating with ephedrine (strong noradrenaline response) and caffeine (strong dopamine response). I was very...

Can someone explain how to create a function that will map an interval of the real line onto some other interval? Is there a general method? Can you demonstrate? (30 140) to (200, 260)? Thanks, Diffy.

Homework Statement Let A=\{(a_\alpha,b_\alpha),\alpha\in I\} be a family of mutually non-intersecting intervals on the real line. Here I is an arbitrary set of indexes. Prove that this family contains at most countably many elements (intervals). Homework Equations None, other than all of...

Can anybody suggest how to write an open interval (a,b) as a combination(union, intersection and compliment) of closed intervals of the form [c,d] and vice versa. What if closed intervals are half closed as following (-inf, f]. 'f' being rational.

Homework Statement Assuming that the random time to failure of a relay is exponentially distributed with a failure rate lambda of 2 x 10^-7 per hour, determin ethe time intervals between failures(years) which have 99%, 95%, 50%, 1%, and 0.1% probabilities of being exceeded Homework...

Good Morning, I am trying to prove that any 2 open intervals (a,b) and (c,d) are equivalent. Show that f(x) = ((d-c)/(b-a))*(x-a)+c is one-to-one and onto (c,d). a,b,c,d belong to the set of Real numbers with a<b and c<d. Let f: (a,b)->(c,d) be a linear function which i graphed to help me...

Homework Statement This is a problem I am just trying to do myself to work out some other problem. I am trying to prove: f:[a, b] → [a, b] Given: f is continuous on [a, b], for all x in [a, b] then df/dx < 1 , f(a) ≥ a , f(b) ≤ b. 2. The attempt at a solution First I proved that...

please help! I need to know the measure of elevation of Antares at 30minute intervals from 7pm to 10.30pm. It's for an assignment and I don't have any idea how to do it. =( Any help at all would be very very very much appreciated.

Hello Enuma et als. I have a few related questions regarding Prediction Intervals for outliers (individual data points). The basic formula that I use is: Mean +/- T(-1df)*sd*sqrt(1+1/n), where Mean is the sample mean, T is the Z-score from the Student's T Distribution Table minus 1 degree of...