Question

$$\begin{gathered} x-\frac{x^3}{6}<x∀x>0 \\ ⇒f\left(x-\frac{x^3}{6}\right)>f\left(\sin x\right)>f\left(x\right) \\ ⇒\frac{f\left(x-\frac{x^3}{6}\right)}{f\left(x\right)}<\frac{f\left(\sin x\right)}{f\left(x\right)}<1 \\ ⇒\underset{x→∞}{lim}\frac{f\left(x-\frac{x^3}{6}\right)}{f\left(x\right)}<\underset{x→∞}{lim}\frac{f\left(\sin x\right)}{f\left(x\right)}<1 \end{gathered}$$