Chapter 3: Derivatives - Section 3.9 - Linearization and Differentials - Exercises 3.9 - Page 175: 45

a. $2\%$ b. $4\%$

Given $dr=0.02r$ for a circle, we have a. circumference: $C=2\pi r, dC=2\pi dr=0.04\pi r$, thus $\frac{dC}{C}=\frac{0.04\pi r}{2\pi r}=0.02$ or $2\%$ b. area: $A=\pi r^2, dA=2\pi r dr=0.04\pi r^2$, thus $\frac{dA}{A}=\frac{0.04\pi r^2}{\pi r^2}=0.04$ or $4\%$