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HMMT 二月 2002 · CALC 赛 · 第 1 题

HMMT February 2002 — CALC Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. 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 .
    d 2
    d →∞
    2 2
    x − ( x + h )
解析

英文解析

  1. 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 .
    d 2
    d →∞
    ( )
    √
    d + d 2
    2ππ
    Solution: This equals lim = .
    d 42
    d →∞
    2 2
    x − ( x + h )