Given any polynomial q$($x$)=a_M{x}^M+a_{M-1}{x}^{M-1}+...+a_1{x}^1+a_0$ then

$\underset{x\frac{+}{-}}{lim}\frac{q(x)}{x^M}=a_M.$

Prove the above limit equation. You may assume that the limit of a sum is the sum of the limits $($when they exist$),$ and that $\underset{x}{lim}{x}^m=0$ if m$<0.$