Word Count : 217

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We need to show that for the given function \( f(x) = e^{\alpha x} \), the \(n\)-th forward difference is: \[ \Delta^n f(x) = (e^{\alpha h} - 1)^n e^{\alpha x}. \] --- ### Step 1: Definition of Forward Difference The forward difference operator \(\Delta\) is defined as: \[ \Delta f(x) = f(x+h) - f(x). ______ __________ ________ ________ _________.
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