sin(x) + cos(x) = root2 sin(pi/4 + x)
/sqt/ Stupid Questions Thread: Oxford Capacity Analysis Edition
Hudson Ward
Gabriel Cooper
that absolute value in the denominator is absolute bullshit
Nolan Garcia
when I get take the function f(x)=1/x and rotate it about the x axis from 1 to infinity I get a solid of revolution with finite volume. My question is can I take the function f(x)=1/x^2 and also rotate it about the x axis on a interval from 1 to infinity to get a solid of revolution with finite volume and why?
Hudson Ross
>My question is can I take the function f(x)=1/x^2 and also rotate it about the x axis on a interval from 1 to infinity to get a solid of revolution with finite volume and why?
Have you tried applying the same reasoning you used to conclude that you get a solid with finite volume by rotating 1/x?
Joseph Watson
Well something tells me the volume is going to be finite too, but truth be told I am not capable of checking myself, so I figured I'd ask here because I am very curious
Hunter Moore
should be [math]\frac{\pi}{3}[/math]
Easton Lewis
A more complete answer. What we're looking for is the value of [eqn]\pi \cdot \int_0^{\infty} x^{-2n}dx[/eqn] for [math]n>0[/math]. Skipping a bunch of limit bullshit this is just [math]\frac{\pi}{2n-1}[/math].
Brayden Scott
should be [eqn]\pi \cdot \int_1^{\infty} x^{-2n}dx[/eqn] sorry about that.
Joseph Ross
stupid fucking question
why is this 2+4/5 and not 2(4/5)?
Jeremiah Wilson
because you're in pre-algebra where people still write mixed fractions instead of improper fractions WHICH TOTALLY IRONICALLY are the preferred form to write rational numbers.