Using differentials, find the approximate values of the following:

Question

Philoid · Accepted Answer

Let us assume that f(x) = sin x

Let so that

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

We know

When, we have.

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

Here, and

∴ Δf = 0

Now, we have

Thus,