SOLUTION: How do you solve functions like these? f(x) = x3 f(x + Δx) − f(x) Δx (Δx ≠ 0)

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Question 1093784: How do you solve functions like these?
f(x) = x3

f(x + Δx) − f(x)
Δx
(Δx ≠ 0)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve functions like these?
f(x) = x^3
f(x + Δx) − f(x) = x^3+3x^2*dx+3x*(dx)^2+(dx)^3 - x^3
Δx
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Divide the difference by dx to get::
= [3x^2*dx + 3x*(dx)^2 + (dx)^3]/dx = 3x^2 + 3x(dx) + (dx)^2)
(Δx ≠ 0)
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If you now take the limit as x approaches zero you get::
= 3x^2
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Cheers,
Stan H.
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