Full function study (variation table, limits, asymptotes)
Questions requiring a comprehensive analysis of a function including computing derivatives, determining monotonicity, constructing a variation table, finding limits, and identifying asymptotes.
In the open interval $(1, e)$, I. The function $\sin ( \ln ( x ) )$ is increasing. II. The function $\cos ( \ln ( x ) )$ is increasing. III. The function $\tan ( \ln ( \mathrm { x } ) )$ is increasing. Which of these statements are true? A) Only I B) Only II C) I and III D) II and III E) I, II and III