1. Two circles have centers that are $d$ units apart, and each has diameter $\sqrt{d}$. For any $d$, let $A(d)$ be the area of the smallest circle that contains both of these circles. Find $\lim _{d \rightarrow \infty} \frac{A(d)}{d^{2}}$.
Solution: This equals $\lim _{d \rightarrow \infty} \frac{\pi\left(\frac{d+\sqrt{d}}{2}\right)^{2}}{d^{2}}=\frac{\pi}{4}$.