Chapter 3.2, Problem 50E

w that if $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+\cdot \cdot \cdot +a_{1}x+a_0$, where $a_0,a_1,\cdot \cdot \cdot \cdot ,a_{n-1}$, and $a_n$are real numbers and $a_n\ne 0$, then $f\left(x\right)$is $\Theta \left(x^n\right)$.

Big-O, big-Theta, and big-Omega notation can be extended to functions in more than one variable. For example, the statement $f\left(x,y\right)$is $O\left(g\left(x,y\right)\right)$means that there exist constantsC, $k_1$, and $k_2$such that $\left|f\left(x,y\right)\right|\le C\left|g\left(x,y\right)\right|$when ever $x>k_1$and $y>k_2$.