Calculus and Its Applications, Chapter 1, 1.2, Section 1.2, Problem 10

Determine the $\displaystyle \lim_{x \to 2} (4x - 5)$ by using the Theorem on Limits of Rational Functions.
When necessary, state that the limit does not exist.


$
\begin{equation}
\begin{aligned}
\lim_{x \to 2} (4x - 5) &= \lim_{x \to 2} 4x - \lim_{x \to 2} 5
&& \text{The limit of a difference is the difference of the limits}\\
\\
&= 4 \cdot \lim_{x \to 2} x - \lim_{x \to 2} 5
&& \text{The limit of a constant times a function is the constant times the limit}\\
\\
&= 4 \cdot \lim_{x \to 2} - 5
&& \text{The limit of a constant is the constant}\\
\\
&= 4 \cdot 2 - 5
&& \text{Substitute 2}\\
\\
&= 8 - 5
&& \text{Simplify}\\
\\
&= 3
\end{aligned}
\end{equation}
$