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HMMT 二月 2004 · CALC 赛 · 第 1 题

HMMT February 2004 — 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. Let f ( x ) = sin(sin x ). Evaluate lim at x = π .
    h → 0 x
解析

英文解析

  1. Let f ( x ) = sin(sin x ). Evaluate lim at x = π .
    h → 0
    Solution: 0 xf ( x + h ) − f ( h ) f ( x ) − f (0)
    The expression is continuous at h = 0, so the limit is just . Lettingx xsin(sin π ) − sin(sin 0)
    x = π yields = 0. π