# lower

1. ### Find the lower bound of the maximal 1x1 square in a 2x2 square

My problem description is a little bit long, I'll try to state it clearly. Assume that we have a 2x2 square, namely $R$, containing many points, each of which has a positive weight. Let $r_{max}$ be the 1x1 square that is inside $R$ and covers points with largest total weights. It is easy to...
2. ### Upper and lower bound.

Hi I have a question. I was trying to find an upper bound for the polynomial x^5-7x^4+15x^3-16x+12 and I did not find one. Is it possible to not have an upper bound? For lower bound I got -1, so generally speaking would -1 be the answer? Or could there be multiple lower boundaries.
3. ### Least upper and greatest lower bounds definition

Hi i am currently working on questions where i am required to determine the least upper bound a set if there is one to do this i have been given the following strategy Given a subset E of R to show that M is the least upper bound, or supremum, of E, check that: 1.x\leq M for all x \in E 2...
4. ### phi > pi/2 = lower half cone?

Working in spherical coordinates, if for example, phi = 3pi/2. Why does that represent the cone in the lower half, and not everything but that cone, since phi is measured from the positive z-axis downwards? Edit: I've looked it up (don't why I didn't do that before posting, my bad) and it...
5. ### Finite approximation using lower sum

I've provided a picture with the question as well as my answer with my work. I got 3.75 or 15/4 but the correct answer was 33/28. What did I do wrong?
6. ### Upper and lower bounds

Need help on this maths question X and Y are continuous values, both measure to 2 significant figures. X=230 and Y=400 Work out the greatest possible value of x/y^2
7. ### Cramer rao lower bound

Hello I desperately need some body to help me in understanding this thing i have tried but i could not get the idea what i am asked to do. I need to find out CRLB please help i am really stuck an confused. The file is attached with.
8. ### Lower Rectangle Method

Hi, Can someone suggest a way to improve the lower rectangle method for area approximation...? I know one way is to increase the number of rectangles so if I put 100 instead of 5 rectangles i will get a better approximation. Any other way it could be improved...? Please don't give other methods...
9. ### Lower and upper derivaties of function at point

Hi guys, I'm looking for a little help with computing the lower and upper derivatives of my function given below, at a point x\in (a, b). f(x) = \sum_{k=1}^{\infty}\left [ {length( (c_{k}, d_{k})\cap (-\infty, x) )} \right ] (where \left \{ (c_{k}, d_{k})_{k=1}^{\infty} \right \} is a...
10. ### Greatest lower and leat upper bound help

what is the least upper bound and greatest lower bound of the set [-1,3] \cap (\sqrt{2} , 5] ? { { x \in {R} : e^{x} \leq 2 } }
11. ### Find lower and upper estimates of integral

Hi, my question is: Consider the integral of 1/(t(t+1)) with respect to t, from lower limit t=0 to the upper limit t=n, where n is an arbitrary positive integer. Let P be the partition {1, 2, ..., n}. Find lower and upper estimates L(P) and U(P) for the integral above. Simplify your answer as...
12. ### laplace equation in lower left quarter

Dears I many refernces of PDEs, we found a fomula solution for laplace equation in the upper half plane or in the right quarter plane, but unfortenatly I did not found a formula for lower left quarteror any method for derived it, Any one has hints about this? in fact my question is part b. in...
13. ### Upper and lower limits

I'm not sure if I'm just totally spacing out or if I'm doing something wrong with this problem but I just cannot figure out how my Professor got these answers. A sample of size n = 21 is used to perform a significance test for H0 : Mu=0 versus Ha : Mu is not = 0. The test statistic is t =...
14. ### Upper and Lower Limits of interval for Riemann's Sum

So i tried to this question and got f(x) = 1 + x upper estimate = 9 lower estimate = 6 wondering if i'm on the right path. thx!
15. ### upper and lower bounds of a set with two variables

I have a problem with writing a decent proof on upper and lower bounds of two sets - A={\frac{n-k^{2}}{n^{2}+k^{3}} , n,k \in \mathbb{N}} and B={\frac{m^{2}-n}{m^{2}+n^{2}} , n,m \in \mathbb{N}, m>n} . I don't know how to cope with these two variables. I want to prove the upper and lower...
16. ### diigraph: lower upper bound of the sum of the weights of n pairwise joint cycles

I have n pairwise joint cycles in a weighted directed graph. For each edge, we have that: $0\leq w_{ij} \leq 1$ (where w_ij is the weight of the (i,j) edge) and for each vertex i, $\sum_j{w_{ij}}\leq 1$ (i.e. the sum of the weights of the outgoing edges is less/equal 1). If we define the weight...
17. ### second derivative of Bessel Function in terms of higher and lower orders of Bessel fn

I have been trying to replicate a result given in a textbook that says J_{n}^{''}(x)=\frac{1}{4}\{J_{n-2}(x)-2J_{n}(x)+J_{n+2}(x)\} where J_{n}(x) is the Bessel Function of the First Kind. Can someone show me how to get this from the recurrence formulae for Bessel derivatives found in the...
18. ### Lower Grade Level for Trig and Algebra ?

Hello, I need some resources or books that can teach Trigonometry and Algebra that relates to vectors, matrices etc at a lower grade level to understand the basics, before moving up the ladder, any online or book suggestions ?
19. ### Proving the lower bound of the order

Hi, I guess this i rather simple task but somehow i cannot get my head arround it. So what i have is a set S of random numbers that are generated in the following way: get a number (random 1-10) for 1 to inf get a number (random 1-10) bigger or equal to the number on a prevoius position...
20. ### glb and lub (greatest lower bound and least upper bound)

Greetings all, I have a question that says S is a bounded set of real numbers and that lub S and glb S are equal. The question wants to know what you can conclude about S (the set). my understanding is that glb and lub are both unique numbers and therefore do not equal. The only thing I could...