Epsilon-delta limits & continuity

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Let $f(x) = 3x + 5$ and fix $c = 4$. Given $\varepsilon = \dfrac{1}{4}$, find the largest $\delta > 0$ such that $|x - c| < \delta$ implies $|f(x) - f(c)| < \varepsilon$.

2. Warm-up

   Let $f(x) = 4x + 5$ and fix $c = 3$. Given $\varepsilon = \dfrac{1}{3}$, find the largest $\delta > 0$ such that $|x - c| < \delta$ implies $|f(x) - f(c)| < \varepsilon$.

3. Warm-up

   Let $f(x) = 6x + 1$ and fix $c = 3$. Given $\varepsilon = \dfrac{1}{6}$, find the largest $\delta > 0$ such that $|x - c| < \delta$ implies $|f(x) - f(c)| < \varepsilon$.

Problems shown under their original terms: Generated (template, solver-computed).