Question

The change in the volume V = x³ of a cube when the edge lengths change from x0 to x0 + dx. The change in the surface area S.

a) 3x0² dx
b) 6x0 dx
c) 9x0² dx
d) 12x0 dx

Answer 1

The change in volume of a cube when the edge lengths change from x0 to x0 + dx can be calculated using the formula 3x0²dx + 3x0(dx)² + (dx)³.

Step-by-step explanation:

The formula for the volume of a cube is V = s³, where s is the length of the side of the cube. To find the change in volume when the edge lengths change from x0 to x0 + dx, we can use the formula for the volume of a cube and calculate the difference between the two volumes:

V(x0 + dx) - V(x0) = (x0 + dx)³ - x0³

Expanding this equation, we get:

• V(x0 + dx) - V(x0) = (x0³ + 3x0²dx + 3x0(dx)² + (dx)³) - x0³
• V(x0 + dx) - V(x0) = 3x0²dx + 3x0(dx)² + (dx)³

Therefore, the change in volume is 3x0²dx + 3x0(dx)² + (dx)³.