Physics
Measurement
Rate of Change and Approximations
11
⚡ Quick Summary
The derivative can be used to calculate approximate changes. If something changes a little bit (ΔR), you can find the approximate change in something else (ΔV) using the rate of change (dV/dR).
dV/dR = 4πR²
ΔV ≈ (dV/dR) * ΔR
The text explains how to find the rate of change of the volume of a sphere with respect to its radius (dV/dR). It then uses this rate of change to approximate the change in volume (ΔV) for a small change in radius (ΔR).