- #1
aclark609
- 35
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I was sifting through the beginning of my book when i came upon a section based on marginals and differentials. My question is why does Δy/Δx ≈ f'(x) when the lim Δx →0 Δy/Δx = f'(x)?
Δx = (x + Δx) - x ; therefore, Δy = f(x + Δx) - f(x) .
Δy/Δx = {f(x + Δx) - f(x)}/ Δx ≈ f'(x)
f'(x) = lim {f(x + Δx) - f(x)}/ Δx
Δx→0
In simplest terms, why does the lim Δx →0 change the ≈ to =?
Δx = (x + Δx) - x ; therefore, Δy = f(x + Δx) - f(x) .
Δy/Δx = {f(x + Δx) - f(x)}/ Δx ≈ f'(x)
f'(x) = lim {f(x + Δx) - f(x)}/ Δx
Δx→0
In simplest terms, why does the lim Δx →0 change the ≈ to =?