HMMT 二月 2002 · CALC 赛 · 第 1 题
HMMT February 2002 — CALC Round — Problem 1
题目详情
- Two circles have centers that are d units apart, and each has diameter d . For any d , A ( d ) let A ( d ) be the area of the smallest circle that contains both of these circles. Find lim . 2 d d →∞ 2 2 x − ( x + h )
解析
- Two circles have centers that are d units apart, and each has diameter d . For any d , A ( d ) let A ( d ) be the area of the smallest circle that contains both of these circles. Find lim . 2 d d →∞ ( ) √ 2 d + d π 2 π Solution: This equals lim = . 2 d 4 d →∞ 2 2 x − ( x + h )