Question

prove that delta - e = 1​

Answer 1

It is true that ∇Δ=Δ∇=δ2, where δf(x)=f(x+h/2)−f(x−h/2) is the central difference.

Step-by-step explanation:

As you have found ∇Δ≠E, since

∇Δf(x)=∇(f(x+h)−f(x))=∇f(x+h)−∇f(x)=(f(x+h)−f(x))−(f(x)−f(x−h))=f(x+h)−2f(x)+f(x−h)≠f(x+h).

It is true that ∇Δ=Δ∇=δ2, where δf(x)=f(x+h/2)−f(x−h/2) is the central difference.