JEE Main 2010Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002Let f:R→Rf:R \to Rf:R→R be a positive increasing function with limx→∞f(3x)f(x)=1\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}} = 1x→∞limf(x)f(3x)=1. Then limx→∞f(2x)f(x)=\mathop {\lim }\limits_{x \to \infty } {{f(2x)} \over {f(x)}} =x→∞limf(x)f(2x)=AOption A. 23{2 \over 3}32BOption B. 32{3 \over 2}23COption C. 3DOption D. 1CheckSkip · show solution
