Let $f:R \to R$ be a positive increasing function with $\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}} = 1$. Then $\mathop {\lim }\limits_{x \to \infty } {{f(2x)} \over {f(x)}} = $

Question

Let $f:R \to R$ be a positive increasing function with

$\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}} = 1$. Then $\mathop {\lim }\limits_{x \to \infty } {{f(2x)} \over {f(x)}} = $

${2 \over 3}$

${3 \over 2}$

Solution

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