Using differentials, find the approximate values of the following: √0.082

Question

Using differentials, find the approximate values of the following:

\(\sqrt{0.082}\)

Answer 1

Let us assume that \(\text{f(x)}=\sqrt{\text{x}}\)

Also, let x = 0.09 so that x + Δx = 0.082

⇒ 0.09 + Δx = 0.082

∴ Δx = –0.008

On differentiating f(x) with respect to x, we get

Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as