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For the following properties it is assumed that each limit \(\underset{x\to a}{\lim}f(x)\) and \(\underset{x\to a}{\lim}g(x)\) exists; furthermore, assume there are no domain violations for the respective given limit.
For the following limits, it is assumed that the functions \(P(x), Q(x)\) are both polynomials whose degrees are \(deg(P(x))=n\) and \(deg(Q(x))=m\)
\(P(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\cdots+a_{2}x^{2}+a_{1}x+a_0\)
\(Q(x)=b_mx^m+b_{m-1}x^{m-1}+b_{m-2}x^{m-2}+\cdots+b_{2}x^{2}+b_{1}x+b_0\)
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