I noticed the 'delta x' is commonly substituted by 'h' in calculus. Is there a particular reason for that? go the letter 'h' was standing for something?

In your pre-rigorous version of derivatives, Fermat offered e, Newton provided o, and also Leibniz offered dx (as go e.g. Euler).

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Seems like Lagrange then offered i (possibly standing because that “increment”?) a bit before 1800, together did Cauchy in the beforehand 1820s.

Lacroix’s introductory calculus textbook supplied k in French (1797) but his English translators provided h rather (1816; this was an important textbook presenting Leibniz’s notation come English readers). There are other instances of h by the 1820s by e.g. Ohm. Yet there to be by no means any solid conventional traditional for at least another several decades beyond that.

It’s not clear to me that it represents anything in particular, beyond being a practically letter the wasn’t a, b, c, d, f, or g, any of which might have to be confusing.

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level 2
· 3y
Differential Geometry

It could have described the horizontal displacement ~ above the graph that a real function, akin to the function of h and k in just how transformations the graphs space taught; that is, if f(x,y)=0 is the equation of some curve in the plane, then the curve shifted appropriate by h and up by k has the equation f(x-h,y-k)=0.

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level 2
· 3y
Every time I check out a write-up like this, I obtain tempted to acquire way right into math history. Thanks for a super amazing response!

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level 2
· 3y
o as in "almost 0 however not quite"?

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level 1
· 3y
Probability

The letter h periodically stands because that 'height', despite that only works below if you turn the graph sideways.

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level 2
· 3y
Computational Mathematics

Boy, this really sounds like something James may would say.

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level 1
· 3y

If you’re referring to just how we extract derivatives through a limit together h has tendency to 0, then I’m pretty certain that h represents nothing in particular.

That’s additionally the just context in i m sorry I’ve seen anyone replace deltaX v h, so i assume it’s simply a random choice that was somehow standardised in high college education. It’s no mandatory, you have the right to use any kind of letter...

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level 2
· 3y

It represents the increment that the live independence variable.

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level 1
· 3y
Could be a reference to the distinction quotient. I need to disagree though; anyone I have actually seen has actually used delta x except for in the DQ

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level 1
· 3y
Differential Geometry

I thought that it to be to protect against confusion around what point is draw close 0, although I have actually seen the in an ext advanced contexts, as in this general an interpretation of a derivative the a function between normed vector spaces:

If a bounded linear map L exists such that lim(|f(x+h)-f(x)-L(h)|/|h|,h,0)=0,

then L is referred to as the "derivative that f in ~ x"; it turns out to it is in unique.

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Even in this case, h have the right to be thought of as Δx, although by that point, Δ often refers come the Laplacian, together an different to ∇2.

The ax "bounded" because that a direct map means if friend look at L(u) for every unit-norm vectors, definition |u|=1, there exists a real number R such that |L(u)|
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