Let f be a differentiable function. Prove that if \(\lim_{x\to\infty} (f(x)+f'(x))=1\), then \(\lim_{x\to\infty} f(x)=1\).

The best solution was submitted by Chiheon Kim (김치헌), 수리과학과 2006학번. Congratulations!

Here is his Solution of Problem 2010-18.

Alternative solutions were submitted by 정성구 (수리과학과 2007학번, +3), 서기원 (수리과학과 2009학번, +3), 심규석 (수리과학과 2007학번, +3), 진우영 (KSA-한국과학영재학교, +3), 박민재 (KSA-한국과학영재학교, +2), 한대진 (?, +2), 문정원 (성균관대학교 수학교육과, +2).