Chapter 7.8, Problem 2E

(a)

To determine

Whether the given function $10x^4+30x+1$ grow faster than $e^x$ as $x\to \infty$ or grow at the same rate as $e^x$ or grow slower than $e^x$.

(b)

To determine

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

(c)

To determine

Whether the given function $\sqrt{1+x^4}$ grow faster than $e^x$ as $x\to \infty$ or grow at the same rate as $e^x$ or grow slower than $e^x$.

(d)

To determine

Whether the given function ${\left(\frac{5}{2}\right)}^x$ grow faster than $e^x$ as $x\to \infty$ or grow at the same rate as $e^x$ or grow slower than $e^x$.

(e)

To determine

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

(f)

To determine

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

(g)

To determine

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

(h)

To determine

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