Chapter 2: Limits and Continuity - Section 2.4 - One-Sided Limits - Exercises 2.4 - Page 74: 14

$$1$$

\begin{align*} \lim _{x \rightarrow 1^{-}}\left(\frac{1}{x+1}\right)\left(\frac{x+6}{x}\right)\left(\frac{3-x}{7}\right) &=\left(\frac{1}{1+1}\right)\left(\frac{1+6}{1}\right)\left(\frac{3-1}{7}\right)\\ &=\left(\frac{1}{2}\right)\left(\frac{7}{1}\right)\left(\frac{2}{7}\right)\\ &=1 \end{align*}