HMMT 二月 2006 · CALC 赛 · 第 2 题
HMMT February 2006 — CALC Round — Problem 2
题目详情
- Compute lim . 2 x → 0 sin( x )
解析
- Compute lim . 2 x → 0 sin( x ) 1 Answer: 2 Solution: Let’s compute all the relevant Maclaurin series expansions, up to the quadratic terms: 1 x cos x 2 2 2 x cos x = x + . . . , e = 1 + x + x + . . . , sin( x ) = x + . . . , 2 so 1 2 x cos x x + . . . e − 1 − x 1 2 lim = lim = . 2 2 x → 0 x → 0 sin( x ) x + . . . 2