Chapter 7.4, Problem 5E

(a)

To determine

Whether the given function ${\log }_{3}x$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(b)

To determine

Whether the given function $\ln 2x$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(c)

To determine

Whether the given function $\ln \sqrt{x}$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(d)

To determine

Whether the given function $\sqrt{x}$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(e)

To determine

Whether the given function $x$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(f)

To determine

Whether the given function $5\ln x$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(g)

To determine

Whether the given function $\frac{1}{x}$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.

(h)

To determine

Whether the given function $e^x$ grow faster than $\ln x$ as $x\to \infty$ or grow at the same rate as $\ln x$ or grow slower than $\ln x$.