Recent content by Poly1

Thanks. Did I read that sometimes \lim_{x \to a^{+}}f(x) and \lim_{x \to a^{-}}f(x) can be different? How's that?

Why did you start with 3.1?

Could someone explain what things like \displaystyle \lim_{x \to 3^+}\frac{1}{x} and \displaystyle \lim_{x \to 3^-}\frac{1}{x} are supposed to be? I googled and it gave me epsilon delta stuff. I'm not smart enough for that. (Doh) I guess I'm asking if anyone could give a dumbed down...

Could you elaborate on this step, please?

Which is greater, $e^{\pi}$ or $\pi^{e}$? I found this when searching for calculus inequalities.

I look forward to it! :D

Can we use Newton's method to approximate the value of definite integrals? (Thinking) EDIT: Ignore if the question doesn't make sense (which it probably doesn't).

Oh I see I mixed the two up. Do you have another delicious question perhaps? (Thinking)

By the way, I enjoyed that question. Thanks guys. Does anyone know more inequalities that be proven with calculus? I found two that look like they could use some calculus (Rofl) 1. $x(1+x)^{-1} < \ln(1+x) < x$ where $-1 < x, \ x \ne 0$. 2. $\alpha (x-1) < x^{\alpha}-1 < \alpha...

I was reading the wiki article on Riemann sums and it says We're using a left Riemann sum, so our sum can never exceed the true value? If we manually calculate the sum of the first 7 sub intervals (and this is indeed greater than 1 according to wolfram), wouldn't that be enough?

Sorry, yes, I should have posted the steps to avoid confusion. You're right I didn't think through my 7 sub intervals guess (Rofl)

Okay, I thought I was meant to approximate the area and show that it goes over $1$. (Doh) I think your set-up and mine are the same since $\displaystyle f(t) = \frac{1}{t}$ therefore $\displaystyle f \left( 1+\frac{2k}{n}\right) = \frac{1}{1+\frac{2k}{n}}.$ I simplified but didn't say so...

Thanks, guys. I get $\displaystyle \int_{1}^{3}\frac{1}{t} \ dt = \lim_{n\to\infty}2\sum_{i=1}^{n}\frac{1}{n+2i}$ I'm not too sure what to do next, though. My guess is this is greater than $ \displaystyle 2\sum_{i=1}^{7}\frac{1}{7+2i} > 1$ but I really don't know. (Thinking)

I'll try to prove the result that I've used. (Thinking)

How do you get $a-b = 0$? I see that $e^{0} = 1$ but that amounts to using we're using what we're proving.