Recent content by Nan1teZ

Homework Statement Determine whether or not the series \sum^{\infty}_{n=1} \frac{1}{\sqrt{n+1}+\sqrt{n}} converges. The Attempt at a Solution Assuming this diverges, I rationalize it to get get \sum^{\infty}_{n=1} \sqrt{n+1} - \sqrt{n}. How would I proceed further? Is this even the...

yeah I got the N = M-L part. But then after that I go in circles trying to show it is < Epsilon. =[ What's the little trick?

Homework Statement Prove or give a counterexample: If {an} and {an + bn} are convergent sequences, then {bn} is a convergent sequence. 2. The attempt at a solution Ok I couldn't think of any counterexamples, so I tried to prove it using delta epsilon definitions: |an - L| < E |an...

Thanks! :D

oops just a stupid mistake!.. okay I got F''(x) = (2*e^(x^2))(1+x^2). If that's wrong I'm going to show the detailed working..

Okay so i get F''(x) = (2*e^(x^2))(1+x) + x Is that right?

Homework Statement Let F(x) = \int^{x}_____________{0} x*e^(t^2) dt for x\in[0,1]. Find F''(x) for x\in(0,1). My only problem is the x, because the interval of the definite integral goes from 0 to x, and x is in the integral, even though the integral is with respect to dt. So I'd just like...

Okay thanks a lot. =)

Okay so tell me if this is right: \left|f(x)-f(a)\right| = \left|\frac{f(x)-f(a)}{x-a}(x-a)\right| = \left|\frac{f(x)-f(a)}{x-a}(0)\right| = 0 < \epsilon Since \lim_{x \to a}\frac{f(x)-f(a)}{x-a}*(x-a) = \lim_{x \to a}\frac{f(x)-f(a)}{x-a}*\lim_{x \to a}(x-a) = \lim_{x \to...

Does that mean we can assume \frac{f(x)-f(a)}{x-a}*(x-a) = 0?

1. The problem statement. Give a complete and accurate \delta - \epsilon proof of the thereom: If f is differentiable at a, then f is continuous at a. 2. The attempt at a solution Known: \forall\epsilon>0, \exists\delta>0, \forall x, |x-a|<\delta \implies \left|\frac{f(x) - f(a)}{x-a}...