Recent content by sinClair

Are you thinking that you just keep on integrating by parts and then that will yield a sum that will be e? I'm having trouble summing up the uv part of the integration... I mean when i do it again I get -b^n*e^-b+e^-1+n(-e^-b*b^n-1+e^-1+integral...) this sums up...?

Homework Statement Show \mathop{\lim}\limits_{n \to \infty}(\frac{1}{n!}\int_{1}^{\infty}x^n\frac{1}{e^x} dx )=1 Homework Equations The hint is that e=\mathop{\lim}\limits_{n \to \infty}\sum_{k=0}^{n}1/k! The Attempt at a Solution First I wrote out the improper integral as limit...

Thank you so much. I was getting confused with changing the limits of integration back and forth but got it now, thanks.

Homework Statement Integrate \int_{0}^{1}\sqrt{\frac{4x^2-4x+1}{x^2-x+3}}dxHomework EquationsThe Attempt at a Solution U sub: let u=x^2-x+3 Then du=2x-1 and then have to evaluate \int_{3}^{3}\sqrt{\frac{du^2}{u}}dx But how with these limits of integration should this be 0? Not sure how to...

Thanks for the suggestion Tinker. Yes that is a convenient case but that also involves using the fundamental theorem of calculus to actually integrate. But for an arbitrary function it's impossible to explicitly calculate the integral like that and get a nice expression to take the limit. So...

Never mind, got it.

Yeah I really should not have pushed the assignment back. But it was a busy week, and I thought I could make it. Had I woke up on time, I would be comfortably done with my major obligations for the week. So part of the frustration was having these high expectations crushed. I feel like...

So I was finishing a problem set early this morning and felt great after I was able to complete it because I had been putting a lot of work into it. I decided to take a short nap before class. But I somehow fell into a deep sleep, and I didn't wake up when my alarm sounded. As a result, I...

Can someone post a link to evaluating higher order total differentials or show how to do it?

Thanks Ivy I got the first part, though I'm not exactly sure how that relates to taylor's theorem. I couldn't see what you wrote for the second quote--mind repeating what you said?

Homework Statement First write f(x,y) = x^2 + xy + y^2 in terms of powers of (x+1) and (y-1) Then write the taylor's formula for f(x,y) a = (1,4) and p=3 Homework Equations We write taylor's formula as: f(x) = f(a) + sum[(1/k!)*D^(k)f(a;h)] + (1/p!)D^(p)f(c;h) where sum is from k=1 to p-1 and...

Ok, got it.

So it turns out I was responsible for some bad arithmetic and got the limit expression wrong. I was really worried when you replied, Ivy! The actual limit is (-2xy^2)/(x^2+y^2)^(3/2) as (x,y)->(0,0). Thanks for the response Ivy. I was not aware of that method of handling limits. But...

Agh, I actually posted the wrong limit. I actually meant (-2xy^2)/sqrt(x^2+y^2).

Homework Statement For a problem I came down to having to show that the limit of (-2xy)/sqrt(x^2+y^2) does not exist as (x,y)->(0,0) Homework Equations The Attempt at a Solution I tried taking iterated limits and showing they are not equal but I still get 0. I also tried...