Recent content by javi438

Is the set S = {(x,y): |x| + |y| <= 2} bounded? If so how do i prove it? looking at the graph i believe that S is bounded by 2 and -2, but I'm not sure if I'm correct and i don't know how to prove it. thanks!

the set S = {(x,y):x and y are rational numbers in [0,1]} has an empty interior

Give an example of a closed set S in R^2 such that the closure of the interior of S does not equal to S (in set notation). I have no idea where to start...any help would be nice! Thanks!

how about in this case? S = {(x,y) : x and y are rational numbers in [0,1]} the closure and boundary of S = [0,1]x[0,1] what would it mean in this case, word for word?

so what would [1,0]x[1,0] mean? the set of (x,y) such that 1<=x<=0 and 1<=y<=0? does the x in between the two [1,0]'s mean anything?

Homework Statement can someone please explan what the line segment [-1,0]x{0} means? i don't understand the notation. if someone could explain it to me it would help me a lot! thanks! Homework Equations The Attempt at a Solution

Homework Statement The limit of (1+a/x)^x as x goes to infinity, where a>0 Homework Equations The Attempt at a Solution I started with saying e^[xln(1+a/x)], but i can't get to the answer e^a please help!

use the mean-value theorem to show that if f is continuous at x and at x+h and is differentiable between these 2 numbers, then f(x+h) - f(x) = f'(x+ah)h for some number a between 0 and 1. mvt: if f is diff'ble on (a,b) and continuous on [a,b] then there is at least one number c in (a,b) for...

Homework Statement A function is decreasing if f(x_{1}) > f(x_{2}) whenever x_{1} < x_{2}, and x_{1}, x_{2} \epsilon \Re a) Show that the set {f(x) : x < a} is bounded below b) Prove that lim (as x goes to a) f(x) = glb{f(x) : x < a} (hint: show that for any \epsilon > 0, there exists...

f(-x) = g(-x) + h(-x) f(-x) = g(x) - h(x) = g(x) + (-h(x)) is that it??

Homework Statement prove that if lim_{x\rightarrow c} f(x) = L, then there are positive numbers A and B such that if 0 < |x-c|< A, then |f(x)|< B 2. The attempt at a solution i know it's something to do with the limit definition, where for \epsilon > 0, there exists a \delta > 0 such...

say function f is continuous on (-\infty,\infty). show that f can be written as f = g + h, where g is an even function and h is an odd function. help pleaseee!

yes I am pretty sureee..because that's what I am learning right nowww :frown:

proof for inequality induction...please help! Homework Statement Prove for all positive integers n that \sum^{n}_{l=1} l^{-1/2} > 2(\sqrt{n+1} -1) 2. The attempt at a solution \sum^{n+1}_{l=1} l^{-1/2} = \sum^{n}_{l=1} l^{-1/2} + (n+1)^{-1/2} > 2(\sqrt{n+1} -1) + (n+1)^{-1/2}...