Answer:
See below.
Step-by-step explanation:
1. f(x) = x - 3
we need to calculate [ f(x + Δx) - f(x)] / Δx
(Δx means a small quantity of x)
For x - 3 we substitute f(x) with x - 3 in the above formula and for f(x +Δx) we substitute x + Δx - 3:-
( x + Δx - 3) - (x - 3) / Δx
= (x - x - 3 + 3 + Δx) / Δx
= Δx / Δx
= 1.
2. x^2 - 2, we have
[(x + Δx)^2 - 2 - (x^2 - 2)] / Δx
(x^2 + 2x Δx + (Δx)^2 - 2 - x^2 + 2) / Δx
= 2xΔx + ( Δx)^2 / Δx
= 2x + Δx.
The others are evaluated n the same way.i
