Recent content by kbrono

Ok thank you for looking it over!

Homework Statement let n\inN To prove the following inequality na^{n-1}(b-a) < b^{n} - a^{n} < nb^{n-1}(b-a) 0<a<b Homework Equations The Attempt at a Solution Knowing that b^n - a^n = (b-a)(b^(n-1) + ab^(n-2) + ... + ba^(n-2) + a^(n-1) we can divide out (b-a) because b-a #...

Homework Statement Define f: [0,\infty) \rightarrow R by f(x) = {0 if x is [0,1] and 1 if x is (1,\infty ) Homework Equations I think if I can show that f is continuous on [0,1] and not continuous on every point of [0,1] then that will suffice. However I have now clue how to go...

Ok here's what I tried Basically I said assume L is not an element of [a,b] Then since f(x) is only defined on the interval [a,b]/{p} Then [a,b]/{p} contains L. Therefore L is an element of [a,b]

Ah ok, thank you

Homework Statement Let f be a function and p\in . Assume that a\leqf(x)\leqb near p. Prove that if L= lim f(x) as x-->p Then L\in [a,b] The Attempt at a Solution I want to say that because f(x) is bounded by [a,b] that automatically implies that the Limit L is also bounded by...

Show that the function f(x)=x is continuous at every point p. Here's what I think but not sure if i can make one assumption. Let \epsilon>0 and let \delta=\epsilon such that for every x\in\Re |x-p|<\delta=\epsilon. Now x=f(x) and p=f(p) so we have |f(x)-f(p)|<\epsilon...

Thank you!

Homework Statement Let f be a function let p /in R. Assume limx->p=L and L>0. Prove f(x)>L/2 The Attempt at a Solution Let f be a function let p /in R. Given that limx->pf(x)=L and L>0. Since L\neq0 Let \epsilon= |L|/2. Then given any \delta>0 and let p=0 we have |f(x)-L| = |0-L| =...

ah, ok so i should expand for each term out to the nth?

Sorry i use a weird notation, f_1(x) denotes the the first term in f(x) f_2(x) denotes second term in f(x). im breaking down f(x) = 1+x and f'(x)=0 + 1 into a term by term format. What I'm doing is setting up a matrix where the first like is f(x) and the second line is x(f'(x)) then using...

I don't this this is an overly complicated proof but it is one I have never seen or done before. Let f be a polynomial with atleast two non-zero terms having different degrees. Prove that the set {f(x),xf'(x)} is linearly independent in P Proof: With out loss of generality we can...

Prove or disprove that each given subset of M2x2 is a subspace of M2x2 under the usual matrix operations. 1. The set of 2x2 matrices that have atleast one row of zeroes. My answer: Not a subspace consider matrix A= 1 2 And matrix B= 0 0...

hmm, I am probably overthinking it then

Yes I accidentally put the definition. The proof is Suppose p,L in R and that f is a function. Show that lim f(x) as x->p = L iff f is defined near p and and for every ep>0 there is a d>0 such that for all x in R with 0<|x-p|<d, |f(x)-L|<ep whenever f(x) is defined.This seems likes its...