# catamite

less info
reputation
210
bio website reddit.com/r/… location meatspace age member for 1 year, 11 months seen 21 hours ago profile views 1,026

when someone smiles at me, all I see is an ape bearing its teethe

# 573 Actions

 Jul16 comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ Ok so past some point $x_0$ or within some neighborhood of a point, that makes sense; thanks! I think I'm going to spend some time proving those identities you listed to help my understanding. Jul16 comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ So when we say $g=O(f)$ what we're saying is g is some element of the set of all functions whose absolute value is bounded by a constant multiple of $f$, is that a correct understanding? Jul16 comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ why can't you then just set A to be the max of your bounded function? Jul16 comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ Also, can I essentially just replace $O(f(x))$ with $Af(x)$ for $A$ some unknown positive constant? Jul16 comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ Thank you Norbert. Could you explain your justification for getting rid of the log in the third equals sign? Jul16 asked Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ Jul16 comment Help Proving that $\frac{(1+\frac{1}{t})^t}{e} = 1 -\frac{1}{2t} + O(\frac{1}{t^2})$ for $t\geq 1$ @did: could you explain the missing step for me? Jul16 accepted Help Proving that $\frac{(1+\frac{1}{t})^t}{e} = 1 -\frac{1}{2t} + O(\frac{1}{t^2})$ for $t\geq 1$ Jul16 comment Help Proving that $\frac{(1+\frac{1}{t})^t}{e} = 1 -\frac{1}{2t} + O(\frac{1}{t^2})$ for $t\geq 1$ Thanks for this, very slick, but could you please quickly explain how you derived the final equality? Jul16 asked Help Proving that $\frac{(1+\frac{1}{t})^t}{e} = 1 -\frac{1}{2t} + O(\frac{1}{t^2})$ for $t\geq 1$ Jul14 comment Why doesn't $2\pi\int_{-1}^1\sqrt{1-x^2}dx$ give the surface area of a sphere of radius $1$? Thanks for the comments and links, they've been a big help. Jul14 asked Why doesn't $2\pi\int_{-1}^1\sqrt{1-x^2}dx$ give the surface area of a sphere of radius $1$? Jul12 revised Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ deleted 77 characters in body Jul12 comment Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ You're right, my mistake, apparently I should be more wary of Wolfram's margin of error. Jul12 comment Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ I checked numerically that removing the 1 makes the inequality untrue, I don't think you can in general integrate the function $|\sin\left(\frac{\pi}{t}\right) -\frac{\pi}{t}\cos\left(\frac{\pi}{t}\right)|$ without first pulling the absolute value bars outside the integral; consider $|x|$ in an interval around zero. Jul12 accepted Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ Jul12 comment Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ Thank you for this! Jul12 comment Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ What it looks like is an elliptic integral (I know nothing about these, beyond apparently what they look like). Jul12 comment Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ Do Carmo's "Differential Geometry of Curves and Surfaces" Section 1-3 problem 9b, the integral is the arc length of a portion of the curve $(t,tsin(\frac{\pi}{t}))$. Jul12 revised Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$ deleted 132 characters in body