Using differentials, find the approximate value of each of the following up to 3 places of decimal.

Question

Philoid · Accepted Answer

Consider y =

Let x = 1 and Δx = -0.001. Then, we get

Δy = (x+∆x)^1/10 - (x)^1/10

Δy = (0.999)^1/10 - 1

(0.999)^1/10 = Δy + 1

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

dy =

= -0.0001

Therefore, the approximate value of is 0.9999.