intervals Definition and 276 Threads

Hello, I'm working on some questions and I need some further explanation; First I must Consider the open interval (0,1), and let S be the set of point in the open unit square; that's is, S={(x,y):0<x,y<1}. Question (a) says Find a 1-1 function that maps (0,1) into, but not necessarily onto, S...

Homework Statement For the function f(x)=xln(x²), x≠0 The Attempt at a Solution f'(x)=2+ln(x²) For the function to be increasing f'(x)>0 2+ln(x²)>0 ln(x²)>-2 x²>e^(-2) Taking square roots of both sides ±x>±(1/e) How can I find the intervals from this? (Somebody has...

Hi all, I originally posted this in the analysis/topology forum but I think this might be a more appropriate place for it. Homework Statement I'm having difficulty proving that all intervals of the real line are connected in the sense that they cannot be decomposed as a disjoint...

I. \sum_{n=1}^{\infty}\frac{n^n}{n!}x^n II. \prod_{n=1}^{\infty}n^x*sin\frac{1}{n^x} I wonder how to find ranges of real values x for convergence to occur in the problems ?? Remark about infinite product:It is said to be convergent if partial products converge to a FINITE and...

Spacelike intervals are when time separation is 0 or the observer measures a single time for the start of two events. Hence the two events are simultaneous to this observer. My question is for this to occur, must the observer be at an equal distance from the two events (or right in the middle of...

It roughly says there exists a continuous function from a normal space X to some interval [a,b] Since the the space is a normal space, there exist two disjoints closed subsets A and B. What I don't understand is how can you associate some abstract space with a real interval and is...

find the intervals of increase and decrease of f(x) = e3x + e-2x. f'(x) = 3e3x - 2e-2x I set f'(x) = 0 to find the critical numbers: 3e3x = 2e-2x 3 ln e3x = 2 ln e-2x 9x = -4x x = 0, which is obviously wrong, (3e^0 - 2e^0 = 1). I found out that I had to combine the two terms using a...

Dear people of this forum, Assume we have an interval of a line [ a, b]. Now, let us divide this interval in many ( infinite ) subintervals of finite size. ? What will be the size of these many intervals, equal or unequal, when the number of subintervals tends to infinite?. ¿there is any...

Im having a problem with curve sketching i can't figure out how to do this problem. I am confused. Heres the question 1. For the following curve find: a)the domain b)the intercepts c)the asymptotes d)intervals of increase or decrease: local maximum and minimum e)concavity and the...

What is the value of za/2 for an 80% confidence interval? a. .255. b. 1.28. c. .0398. d. .525. i know the answer is a, but does anyone know how to calculate that :blushing: ?

Heres the problem: Mr. K would like to know what percentage of the senior class has watched the movie Groundhog Day. He would like to be sure to within 0.05 or 5%. He wants to compute a 90% confidence interval. How many students must he poll in order to achieve these goals? Help Please...

I am a computer scientist that only recently got interested in topology. I have got the following question: How to prove, in an elegant way, that an arbitrary sum of open intervals (a, b), where a is in R and b is in R, is open? I have got some kind of a proof, but I am not sure it is...

Hello. I am teaching myself statistics and my question is about confidence intervals. I understand that I can accept or reject a null hypothesis based on comparing my p values to the significance value (say .05) But how do i accept or reject a null hypothesis based SOLELY on a given...

Find the intervals containing the soltuions for 4x^2 - e^x = 0 now this can't be solved by elementary methods since all i get is x - 2 \ln(x) = \ln(4) finding the derivative doesn't help either f'{x} = 8x - e^x 0 = 8x - e^x cant just GUESS ... that isn't right ... this is...

Hello everyone, I'm back again...haha. I was just checking over my homework assignment again and realized that I'm pretty unsure of one of the assigned problems. Here it is: Find the Intervals of Increase and Decrease, local max and min values and the concavity of the function f(x)=...

"If I and J are bounded, then I\capJ is also bounded." Now, I was able to do this using the definition of suprema and infima and so fourth, but it is one godawful mess. I could sumbit it as is, but I was wondering if there's an easier way.

If I_n = (0, 1/n) where n is any natural no. is a sequence of nested intervals, then the intersection of all the I_n is empty. I was able to get the proof similar as that of above problem but the I_n is closed, that is, I_n = [0, 1/n]... and further, the intersection of all the I_n is...

ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2 I'm still trying to figure it out. What I was thinking, you're always moving through spacetime at c, right? Through time, but that will be less when traveling in spatial demensions. (If any of this is wrong, let me know, I read this somewhere but can't...

so if I want to find the 90% confidence interval..how do I do it? all I know is that given 220 salads, 179 were contaminated. i'm asked to find the 90% confidence interval, the true proportion of the contimatned salads. so the formula is 100(1- a)% confidnece =[(y - z(a/2) *...

once you find the intervals of Increase/Decrease in a function how do u graph that??

Hello all If you are given the function y = x - 3e^-x^2 and you want to find the intervals where the function is increasing and decreasing, concavity, inflection points and any local extreme values, would I first find the derivative? My work If f(x) = x - 3e^-x^2 then f'(x) =...

On what intervals is y= l 2-x l increasing or decreasing?? Wouldnt it be its always increasing cause of the absolute symbol, but that's not the answer. Also find where x/(x^2) - 1 is increasing/decreasing?? Given tan(xy)= x^2, find y' y' of (sinx)^x

Easy question but I'm being stupid somewhere. quite frustrating... enough to post it :surprise: Basically the question is Semiconductor wafer testing: 365 dies, 201 passed probing. Assuming stable process calculate a 95% confidence interval for the proportion of all dies that pass the...

Ok, I'm very new to calculus, and was stuck on the very basics of it. I'm only 14, but am extremely interested in math and science. I was inspired to study calculus when reading a book named, "Five Equations that changed the World", by Michael Guillen. Now I was doing some problems involving...

Please look at: http://mathworld.wolfram.com/Interval.html My question is about this line: "If one of the endpoints is +-oo , then the interval still contains all of its limit points, so (-oo,b] and [a,oo) are also closed intervals". How come ?

I'm currently taking multivariable calculus and we're studying double and triple integration. The actual integration itself is easy, but what I am not understanding at all is how to find the intervals for integration. I can only manage to find them on only the most simple problems. I don't need...