QuestionProve that $\lim _{x \rightarrow 6}\left(\frac{1}{7} x-9\right)=-\frac{57}{7}$ by finding $\delta$ for any $\varepsilon>0$.

Studdy Solution
From the last inequality, we can see that if we choose $\delta =7\varepsilon$, then $\frac{1}{7}|x -6| = |x -6|/7 < \varepsilon$ whenever $0 < |x -6| <7\varepsilon$.
So, we can choose $\delta =7\varepsilon$.