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


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.


1
1