Chapter 7.4, Problem 4E

(a)

To determine

Whether the given function $x^2+\sqrt{x}$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(b)

To determine

Whether the given function $10x^2$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(c)

To determine

Whether the given function $x^2{e}^{-x}$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(d)

To determine

Whether the given function ${\log }_{10}\left(x^2\right)$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(e)

To determine

Whether the given function $x^3-x^2$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(f)

To determine

Whether the given function ${\left(\frac{1}{10}\right)}^x$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(g)

To determine

Whether the given function ${\left(1.1\right)}^x$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(h)

To determine

Whether the given function $x^2+100x$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.