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HMMT 二月 2004 · CALC 赛 · 第 1 题

HMMT February 2004 — CALC Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

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