Chapter 7.8, Problem 3E

(a)

To determine

Whether the given function $x^2+4x$ 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 $x^5-x^2$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(c)

To determine

Whether the given function $\sqrt{x^4+x^3}$ 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 ${\left(x+3\right)}^2$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.

(e)

To determine

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

(f)

To determine

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

(h)

To determine

Whether the given function $8x^2$ grow faster than $x^2$ as $x\to \infty$ or grow at the same rate as $x^2$ or grow slower than $x^2$.