(Untitled)

[calcnerd256]

so, i found something interesting in my econ book and i wanted to know if it was always true

notation
let [a,b] = the closed interval from a to b
let (integral r) phi = the integral over the interval r of the function phi
let d = lim (epsilon->0+) delta

given a function f over Rlet g(x) = ( (integral [zero, x]) f(t) * dt ) / x

Comments

[calcnerd256]

note the past tense on "wanted"
i proved it, so don't worry about telling me it's always true
it's as true as the leaves on the proof tree (not shown)

[calcnerd256]

okay, i know why it's true now
f represents the values being pumped into the numerator
x is the denominator
so it's like gpa
if f > g, g' > 0
etc etc mutatis mutare

[calcnerd256]

that's mutatis mutandis, i think
i'll ask courtney

[calcnerd256]

so that means there exists a phi such that
phi(x) < 0 <=> x < 0
phi(0) = 0
phi(x) > 0 <=> x > 0
g'(x) = phi((f - g)(x))

[calcnerd256]

so that means there exists a φ such that
φ(x) < 0 <=> x < 0
φ(0) = 0
φ(x) > 0 <=> x > 0
g'(x) = φ((f - g)(x))