Q. 9 A5.0( 1 Vote )

# Using differentials, find the approximate values of the following:

Answer :

Let us assume that

Also, let x = 25 so that x + Δx = 25.02

⇒ 25 + Δx = 25.02

∴ Δx = 0.02

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 = 0.02

⇒ Δf = (0.1)(0.02)

∴ Δf = 0.002

Now, we have f(25.02) = f(25) + Δf

⇒ f(25.02) = 5 + 0.002

∴ f(25.02) = 5.002

Thus,

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If y = sin x and x changes from to, what is the approximate change in y?

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