Chapter 11.5, Problem 42E

(a)

To determine

To prove: $e^{kx}>\frac{k^2{x}^2}{2}$, for $k$ be a positive constant.

(b)

To determine

To prove: The statement $e^{kx}>\frac{k^2{x}^2}{2}\text{for}k>0$ is deduced to $e^{-kx}>\frac{2}{k^2{x}^2}\text{for}x>0$.

(c)

To determine

To prove: $x{e}^{-kx}$ approaches to $0\text{as}x\to \infty$.