Using differentials, find the approximate values of the following:
Let us assume that
Also, let x = 25 so that x + Δx = 26
⇒ 25 + Δx = 26
∴ Δx = 1
On differentiating f(x) with respect to x, we get
We know
When x = 25, 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 Δx = 1
⇒ Δf = (0.1)(1)
∴ Δf = 0.1
Now, we have f(26) = f(25) + Δf
⇒ f(26) = 5 + 0.1
∴ f(26) = 5.1
Thus,