Q12Advanced Engineering Mathematics

Question

Show that Δ^{2} e^{x} = (e - 1)^{2} e^{x}; interval of differencing being unity.

Answer 1

The first forward difference of $e^{x}$ is defined as $Δ e^{x} = e^{x + h} - e^{x}$ . If the interval of differencing $h = 1$ , then $Δ e^{x} = e^{x + 1} - e^{x} = e^{x} (e - 1)$ . The second forward difference is the difference of the first difference: $Δ^{2} e^{x} = Δ (Δ e^{x}) = Δ (e^{x} (e - 1))$ . Since $(e - 1)$ is a constant, we can pull it out: $(e - 1) Δ e^{x} = (e - 1) [e^{x} (e - 1)] = (e - 1)^{2} e^{x}$ .

Q12Advanced Engineering Mathematics

Question

Answer