Recent content by spenghali

right right, i should have noticed that

Homework Statement A velocity selector consists of electric and magnetic fields described by the expressions vector E = E k-hat and vector B = B j-hat, with B = 0.0130 T. Find the value of E such that a 830 -eV electron moving along the negative x-axis is undeflected? Homework Equations...

ok, so i figured out #1, I used the fact that |fn(x)| is less than or equal to bn if and only if it is greater than or equal to -bn, and less than or equal to bn, then applied the squeeze theorem. Still working on #2

For #1, we know that bn converges to zero, and thus by definition of convergence, i can pick N = eps. The fact that bn is only convergent and not uniformly convergent is confusing me as to why fn(x) being less than or equal to bn implies UNIFORM convergence.

Homework Statement 1.) Prove that if { f_{n} } is a sequence of functions defined on a set D, and if there is a sequence of numbers b_{n}, such that b_{n} \rightarrow 0, and | f_{n}(x) | \leq b_{n} for all x \in D, then { f_{n} } converges uniformly to 0 on D. 2.) Prove that if { f_{n} } is a...

Cool, thanks for the input.

Homework Statement Note: I will use 'e' to denote epsilon and 'd' to denote delta. Using only the e-d definition of continuity, prove that the function f(x) = x/(x+1) is uniformly continuous on [0, infinity). Homework Equations The Attempt at a Solution Proof: Must show...

thanks for the input, unfortunately my professor refused to tell me if i was right.

Homework Statement If limsup(an) and limsup(bn) are finite, prove that limsup(an+bn) \leq limsup(an) + limsup(bn). Homework Equations The Attempt at a Solution My proof seems a bit short, so if someone could please reassure me this is a valid proof, thanks in advance. Proof...

ah yes, thanks for the tip.

Homework Statement If a_{1} = 1 and a_{n+1} = (1-(1/2^{n})) a_{n}, prove that a_{n} converges. Homework Equations NONE The Attempt at a Solution I am confident about my attempt, I just want it checked. Thanks. First show that a_{n} is monotone: a_{n} = {1, 1/4, 21/32...