/sci/ - Science & Math » Thread #12696892

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Anonymous Fri 12 Feb 10:15:32 2021 No.12696892 View Reply Original Report

Quoted By: >>12696906 >>12696907

Is y = -integral(1/f'(x)) orthogonal to y = f(x) at every point?

Anonymous

Anonymous Fri 12 Feb 2021 10:26:57 No.12696902 Report

Quoted By:

Maybe

Anonymous

Anonymous Fri 12 Feb 2021 10:29:57 No.12696906 Report

Quoted By:

>>12696892
Firstly those are equations so saying they are orthogonal makes no sense. What you are probably trying to ask is whether the curves

$t \to \left(t,-\int_{0}^t \frac{1}{f'(x)} dx \right)$
$t \to \left(t,f(t) \right)$
are othogonal.

For that you have to look at the tangent vectors which are
$\left(1,-\frac{1}{f'(t)} \right)$
$\left(1, f'(t) \right)$
The scalar product of them is zero for each $t$ so they are indeed orthogonal. Assuming of course that everything is defined.

Anonymous

Anonymous Fri 12 Feb 2021 10:30:15 No.12696907 Report

Quoted By:

>>12696892
orthogonal in what sense?
Have you tried f=id?

Anonymous

Anonymous Fri 12 Feb 2021 10:40:45 No.12696923 Report

Quoted By:

Ah, I suppose this can be generalized as such:

if $g\in G$ is in a group and $d$ any auto, then

$d(g) * d(d^{-1}(d(g)^{-1})) = e$

and you were asking it in the form
>is d of g times d of $d^{-1}(d(g)^{-1})$ the unit?

Anonymous

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Anonymous Fri 12 Feb 2021 10:41:00 No.12696925 Report

Quoted By:

This is orthogonal to y = sinx at every value of x.

Quite pretty.

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