HMMT 二月 1998 · CALC 赛 · 第 4 题
HMMT February 1998 — CALC Round — Problem 4
题目详情
英文原题
Question Four . [4 points]
f ( x ) dx 1
2 3
∫
x x x
Let f ( x ) = 1 + + + +… , for − 1 ≤ x ≤ 1 . Find e .0
2 4 8
解析
英文解析
- Problem: Let f ( x ) = 1 + + + + . . . , for − 1 ≤ x ≤ 1. Find e .
2 4 8
1 2
Solution: Observe that f ( x ) is merely an infinite geometric series. Thus f ( x ) = = . Thenx
1 − 2 − x
∫2
√ √1
2 ln 2 22 = 2 ln 2. Then e = 2 = 2 .
2 − xx 0
sin(1 − x )