My professor just told me that if [tex]\Delta x[/tex] is small, then we can expand [tex]L(x+\Delta x)[/tex] as follows:(adsbygoogle = window.adsbygoogle || []).push({});

[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.

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# Could someone please explain this (simple) fact about Taylor expansions?

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