Recent content by barksdalemc

Is there a way other than trial and error to tell whether an integrating factor h is a function of x only, y only, or of x and y?

I need to integrate e^abs(x-5) I'm confused as to how I can treat the absolute value in the exponent. Can I split it up between X<5 and X>5?

Yes I am required to use the definition of the limit. I was going to use the fact that sin x is bounded. Can I say |X^2sin(1/X) - Xo^2sin(1/Xo)| is always less than or equal to |X^2-Xo^2|? Then I can choose an epsilon that works for f(x)=X^2 to show continuity.

Correct, but I am given only the interval (0,1). At the least I need to show continuous in that interval. Not sure what choice of eps for this function.

Homework Statement Show that f(x)=x^2sin(1/x) is piecewise continuous in (0,1) The Attempt at a Solution I'm trying to show continuity in (0,1) so I need to show limit as function approaches any given Xo is the value of the function itself, ie. |X^2sin(1/X) - Xo^2sin(1/Xo)|< eps. Can...

yes that is exactly where I am confused, but he is saying that f(p/n) > eps. f(p/n) given 1/n.

Homework Statement Consider the Dirichelet's function defined on (0,1) by f(x)= 0 is x is irrational and f(x)= 1/q if x=p/q where p and q are positive integers with no common factors. Show that lim f(x) for any x in (0,1) is 0 The Attempt at a Solution Here is the first line of...

Halls of Ivy, I meant for theorems which state if and only if. Are there if and only if statements where the logic cannot backwards?

If I prove one direction, is the proof in the other direction just the logic going the other way? In any case, let's say I want to show it is convex given for every x,y in (a,b), f(y)-f(x)>= (y-x)f'(x)

Homework Statement Let f be differentiable on (a,b). Show that f is convex if and only if for every x,y in (a,b), f(y)-f(x)>= (y-x)f'(x) The Attempt at a Solution The mean value theorem says that there exists an x' in (a,b) such that f'(x') is the average rate of change of the functions...

Homework Statement Show that lim(h-->0) [f(x+h)-2f(x) + f(x-h)]/h^2 is equal to f''(x) for any given value of x where the second derivative exists. I'm supposed to use L'Hopitals rule for this problem. I did and got [f(x+h)-f(x-h)]/2h Now I am stuck. I thought about adding and...

Homework Statement Show that Lipschitz continutity imples uniform continuity. In particular show that functions sinx and cosx are uniformly continuous in R. The Attempt at a Solution I said that if delta=epsilon/k that Lipschitz continuity imples continuity. Now I am stuck as to how to...

I'm trying to understand in the context of probability distributions. What the convolution of the sum of two random variables represents.

Can someone explain convolution to me. I have read three different books and gone to office hours and am not getting the fundamentals.

I did a few problems in integration by parts. There are two that I just can't seem to get. I've tried every type of subsitution or part I can think of. 1. e^sqrt(x) 2. sin (ln x)