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In my textbook they derive that a solution to the law of Faraday and the law of Ampère-Maxwell is an electromagnetic wave.

In one of the steps they have to calculate [tex]E(x+dx,t)[/tex] where E is the magnitude of the electric field of the wave. They say

[tex]E(x+dx,t) \approx E(x,t)+\frac{dE}{dx} \Big|_{t=constant}dx[/tex]

On what theorem is this step based?

Thank you.

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# Approximation with derivative

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