Question

Find he change in the volume of a cube when the edge lengths all change by an amount dx

Answer 1

Hello,

Method 1:

V=x^3
dV=3x²*dx

Method 2:

V+dV=(x+dx)^3=x^3+3x^2dx+3xdx²+dx^3
V=x^3

V+dV-V=dV=3x²dx+3xdx²+dx^3
Since dx^3<<dx^2<dx , we forget dx^3 and dx^2
==>dV=3x²dx