Question

Consider a square with sides of length "s" and area "A." If the side length is changed by "Δs," which of the following best approximates the change in area? a. ΔA = Δs b. ΔA = 2Δs c. ΔA = sΔs d. ΔA = s^2Δs

Answer 1

Hi,

Explanation:

If one side length is changed, area 's change will be

`\Delta\ A=(s+\Delta\ s )*s-s^2=s*\Delta\ s.\\`

If both side length are changed, area 's change will be

`\Delta\ A=(s+\Delta\ s)^2-s^2=2s\ \Delta s+(\Delta \ s)^2`