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[tex]

L(x + \Delta x) = L(x) + \frac{d L}{d x} \Delta x + \frac{1}{2!} \frac{d^2 L}{d x^2} (\Delta x)^2 + \ldots,

[/tex]

where each of the derivatives above is evaluated at [tex]x[/tex]. Could someone please explain why this is true? I just can't see it. Thanks.