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*}
To do
- Limits by direct substitution activity (Khan Academy)
More info
- Limit properties (Study Support, USQ Library)
- Limit properties video (Khan Academy)