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 = 256 and Δx = -1. Then, we get

Δy = (x+∆x)^1/4 - (x)^1/4

= (225)^1/4 - (256)^1/4

= (225)^1/4 - 4

= (225)^1/4 = Δy + 4

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

= -0.0039

Therefore, the approximate value of (255)^1/4 is 3.9961.