Find the approximate change in the value of , when x changes from x = 2 to x = 2.002.

Question

Philoid · Accepted Answer

Let

Δx and Δy are very small changes in x and y respectively.

As x changes from 2 to 2.002

x = 2

Δx = 2.002 – 2 = 0.002

The change Δy with change Δx is given by

Let us find

y = x^-2

Substitute in (i)

Substitute values x = 2 and Δx = 0.002

⇒ Δy = -0.0005

As Δy is negative which implies y decreases.

Hence y decreases by 0.0005 as x goes from 2 to 2.002.