Question

Can you evaluate something like this?

Answer 1

See below.

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