Question

use differential to approximate fourth root of 81.5

Answer 1

y = x raise to power 1/4
x= 81.5
dx = 0.5
so that x+dx=81.5
now y +dy = (x +dx) raise to power 1/4
dy = (x+dx) raise to power 1/4 -y = (81.5) raise to power 1/4 - 3
(81.5) raise to power 1/4 = dy + 3
and dy= dy/dx(dx)= 1/4x raise to power -3/4 dx
= 1/4x raise to power 3/4 dx
= 1/4(81) raise to power 3/4(0.5)
=1/4*27 (0.5)
= 1/108(0.5)
=0.009*0.5
=0.0045
=(81.5) raise to power 1/4 = 0.0045+3
=3.0045