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Limits

Limit properties

An example of using the limit properties:
\( \newcommand{\eqncomment}[2]{\small{\text{ #2}} } 
\newcommand{\ceqns}{\begin{array}{rcll}}
\newcommand{\ceqne}{\end{array}} \)

\begin{eqnarray*}  
&& \lim_{x\rightarrow 3} \left( 2x^{3} + 5 \right) \\
&=& \lim_{x\rightarrow 3} \left(2x^{3}\right) + \lim_{x\rightarrow 3} 5 & \eqncomment{0.5}{ addition property} \\
&=& 2 \times \lim_{x\rightarrow 3} \left( x^{3} \right) + \lim_{x\rightarrow 3} 5 & \eqncomment{0.5}{scalar multiplication property} \\
&=& 2 \times 3^{3} + 5 & \eqncomment{0.4}{power law and constant}\\&&&\eqncomment{0.5}{ property} \\
&=& 59
\end{eqnarray*}

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