Question

Using differentials, find the approximate value of each of the following.

(a) (b)

Answer 1

(a) Consider

Then,

Now, dy is approximately equal to Δy and is given by,

Hence, the approximate value of = 0.667 + 0.010

= 0.677.

(b) Consider. Let x = 32 and Δx = 1.

Then,

Now, dy is approximately equal to Δy and is given by,

Hence, the approximate value of

= 0.5 − 0.003 = 0.497.